Solve for x 151=235x-16x^2

$151 = 235 x - 16 x^{2}$

Rewrite the equation as $235 x - 16 x^{2} = 151$ .

$235 x - 16 x^{2} = 151$

Subtract $151$ from both sides of the equation.

$235 x - 16 x^{2} - 151 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = - 16$ , $b = 235$ , and $c = - 151$ into the quadratic formula and solve for $x$ .

$\frac{- 235 \pm \sqrt{235^{2} - 4 \cdot (- 16 \cdot - 151)}}{2 \cdot - 16}$

Simplify.

Simplify the numerator.

Raise $235$ to the power of $2$ .

$x = \frac{- 235 \pm \sqrt{55225 - 4 \cdot - 16 \cdot - 151}}{2 \cdot - 16}$

Multiply $- 4$ by $- 16$ .

$x = \frac{- 235 \pm \sqrt{55225 + 64 \cdot - 151}}{2 \cdot - 16}$

Multiply $64$ by $- 151$ .

$x = \frac{- 235 \pm \sqrt{55225 - 9664}}{2 \cdot - 16}$

Subtract $9664$ from $55225$ .

$x = \frac{- 235 \pm \sqrt{45561}}{2 \cdot - 16}$

Multiply $2$ by $- 16$ .

$x = \frac{- 235 \pm \sqrt{45561}}{- 32}$

Simplify $\frac{- 235 \pm \sqrt{45561}}{- 32}$ .

$x = \frac{235 \pm \sqrt{45561}}{32}$

The final answer is the combination of both solutions.

$x = \frac{235 + \sqrt{45561}}{32}, \frac{235 - \sqrt{45561}}{32}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{235 + \sqrt{45561}}{32}, \frac{235 - \sqrt{45561}}{32}$

Decimal Form:

$x = 14.01406963 \dots, 0.67343036 \dots$