9v(v+7)=83

Solution for 9v(v+7)=83 equation:

9v(v+7)=83

We move all terms to the left:

9v(v+7)-(83)=0

We multiply parentheses

9v^2+63v-83=0

a = 9; b = 63; c = -83;
Δ = b2-4ac
Δ = 632-4·9·(-83)
Δ = 6957
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6957}=\sqrt{9*773}=\sqrt{9}*\sqrt{773}=3\sqrt{773}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-3\sqrt{773}}{2*9}=\frac{-63-3\sqrt{773}}{18}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+3\sqrt{773}}{2*9}=\frac{-63+3\sqrt{773}}{18}
$