(V-4)^2=2v^2-11v-2

Solution for (V-4)^2=2v^2-11v-2 equation:

(-4)^2=2V^2-11V-2

We move all terms to the left:

(-4)^2-(2V^2-11V-2)=0

We add all the numbers together, and all the variables

-(2V^2-11V-2)+16=0

We get rid of parentheses

-2V^2+11V+2+16=0

We add all the numbers together, and all the variables

-2V^2+11V+18=0

a = -2; b = 11; c = +18;
Δ = b2-4ac
Δ = 112-4·(-2)·18
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{265}}{2*-2}=\frac{-11-\sqrt{265}}{-4}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{265}}{2*-2}=\frac{-11+\sqrt{265}}{-4}
$