(V-7)^2=2v^2-24v+73

Solution for (V-7)^2=2v^2-24v+73 equation:

(-7)^2=2V^2-24V+73

We move all terms to the left:

(-7)^2-(2V^2-24V+73)=0

We add all the numbers together, and all the variables

-(2V^2-24V+73)+49=0

We get rid of parentheses

-2V^2+24V-73+49=0

We add all the numbers together, and all the variables

-2V^2+24V-24=0

a = -2; b = 24; c = -24;
Δ = b2-4ac
Δ = 242-4·(-2)·(-24)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{6}}{2*-2}=\frac{-24-8\sqrt{6}}{-4}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{6}}{2*-2}=\frac{-24+8\sqrt{6}}{-4}
$