Solve Using the Quadratic Formula 3x^2=5x+8

$3 x^{2} = 5 x + 8$

Step 1

Move all the expressions to the left side of the equation.

Subtract $5 x$ from both sides of the equation.

$3 x^{2} - 5 x = 8$

Subtract $8$ from both sides of the equation.

$3 x^{2} - 5 x - 8 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 3$ , $b = - 5$ , and $c = - 8$ into the quadratic formula and solve for $x$ .

$\frac{5 \pm \sqrt{{(- 5)}^{2} - 4 \cdot (3 \cdot - 8)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 5$ to the power of $2$ .

$x = \frac{5 \pm \sqrt{25 - 4 \cdot 3 \cdot - 8}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 8$ .

Multiply $- 4$ by $3$ .

$x = \frac{5 \pm \sqrt{25 - 12 \cdot - 8}}{2 \cdot 3}$

Multiply $- 12$ by $- 8$ .

$x = \frac{5 \pm \sqrt{25 + 96}}{2 \cdot 3}$

Add $25$ and $96$ .

$x = \frac{5 \pm \sqrt{121}}{2 \cdot 3}$

Rewrite $121$ as $11^{2}$ .

$x = \frac{5 \pm \sqrt{11^{2}}}{2 \cdot 3}$

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

$x = \frac{5 \pm 11}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{5 \pm 11}{6}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{8}{3}, - 1$