Solve Using the Quadratic Formula 3x^2-2x-5=0

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Algebra

$3 x^{2} - 2 x - 5 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 3$ , $b = - 2$ , and $c = - 5$ into the quadratic formula and solve for $x$ .

$\frac{2 \pm \sqrt{{(- 2)}^{2} - 4 \cdot (3 \cdot - 5)}}{2 \cdot 3}$

Simplify.

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Simplify the numerator.

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Raise $- 2$ to the power of $2$ .

$x = \frac{2 \pm \sqrt{4 - 4 \cdot 3 \cdot - 5}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$x = \frac{2 \pm \sqrt{4 - 12 \cdot - 5}}{2 \cdot 3}$

Multiply $- 12$ by $- 5$ .

$x = \frac{2 \pm \sqrt{4 + 60}}{2 \cdot 3}$

Add $4$ and $60$ .

$x = \frac{2 \pm \sqrt{64}}{2 \cdot 3}$

Rewrite $64$ as $8^{2}$ .

$x = \frac{2 \pm \sqrt{8^{2}}}{2 \cdot 3}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{2 \pm 8}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{2 \pm 8}{6}$

Simplify $\frac{2 \pm 8}{6}$ .

$x = \frac{1 \pm 4}{3}$

The final answer is the combination of both solutions.

$x = \frac{5}{3}, - 1$

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Name

Name	one billion three hundred ninety-nine million two hundred forty-two thousand seven hundred fifty-one

Interesting facts

1399242751 has 8 divisors, whose sum is 1415007104
The reverse of 1399242751 is 1572429931
Previous prime number is 1153

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 43
Digital Root 7

Name

Name	seventy-one million one hundred ninety-three thousand fifty-eight

Interesting facts

71193058 has 16 divisors, whose sum is 109836000
The reverse of 71193058 is 85039117
Previous prime number is 89

Basic properties

Is Prime? no
Number parity even
Number length 8
Sum of Digits 34
Digital Root 7

Name

Name	one billion five hundred eighty-five million two hundred thirty-three thousand two hundred fifty-six

Interesting facts

1585233256 has 32 divisors, whose sum is 5361344640
The reverse of 1585233256 is 6523325851
Previous prime number is 479

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 40
Digital Root 4

Factor y^2-4

Simplify i^66

Solve Using the Square Root Property (x-3)^2=5

Evaluate square root of -300

Graph (x^2)/9-(y^2)/16=1