Solve Using the Quadratic Formula 8t^2+6t=35

$8 t^{2} + 6 t = 35$

Step 1

Subtract $35$ from both sides of the equation.

$8 t^{2} + 6 t - 35 = 0$

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 $a = 8$ , $b = 6$ , and $c = - 35$ into the quadratic formula and solve for $t$ .

$\frac{- 6 \pm \sqrt{6^{2} - 4 \cdot (8 \cdot - 35)}}{2 \cdot 8}$

Step 4

Simplify.

Simplify the numerator.

Raise $6$ to the power of $2$ .

$t = \frac{- 6 \pm \sqrt{36 - 4 \cdot 8 \cdot - 35}}{2 \cdot 8}$

Multiply $- 4 \cdot 8 \cdot - 35$ .

Multiply $- 4$ by $8$ .

$t = \frac{- 6 \pm \sqrt{36 - 32 \cdot - 35}}{2 \cdot 8}$

Multiply $- 32$ by $- 35$ .

$t = \frac{- 6 \pm \sqrt{36 + 1120}}{2 \cdot 8}$

Add $36$ and $1120$ .

$t = \frac{- 6 \pm \sqrt{1156}}{2 \cdot 8}$

Rewrite $1156$ as $34^{2}$ .

$t = \frac{- 6 \pm \sqrt{34^{2}}}{2 \cdot 8}$

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

$t = \frac{- 6 \pm 34}{2 \cdot 8}$

Multiply $2$ by $8$ .

$t = \frac{- 6 \pm 34}{16}$

Simplify $\frac{- 6 \pm 34}{16}$ .

$t = \frac{- 3 \pm 17}{8}$

Step 5

The final answer is the combination of both solutions.

$t = \frac{7}{4}, - \frac{5}{2}$