(V-5)^2=2v^2-7v+27

Solution for (V-5)^2=2v^2-7v+27 equation:

(-5)^2=2V^2-7V+27

We move all terms to the left:

(-5)^2-(2V^2-7V+27)=0

We add all the numbers together, and all the variables

-(2V^2-7V+27)+25=0

We get rid of parentheses

-2V^2+7V-27+25=0

We add all the numbers together, and all the variables

-2V^2+7V-2=0

a = -2; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·(-2)·(-2)
Δ = 33
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{-(7)-\sqrt{33}}{2*-2}=\frac{-7-\sqrt{33}}{-4}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{33}}{2*-2}=\frac{-7+\sqrt{33}}{-4}
$