(v-1)2=2v2+v-27

Solution for (v-1)2=2v2+v-27 equation:

(v-1)2=2v^2+v-27

We move all terms to the left:

(v-1)2-(2v^2+v-27)=0

We multiply parentheses

2v-(2v^2+v-27)-2=0

We get rid of parentheses

-2v^2+2v-v+27-2=0

We add all the numbers together, and all the variables

-2v^2+v+25=0

a = -2; b = 1; c = +25;
Δ = b2-4ac
Δ = 12-4·(-2)·25
Δ = 201
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{-(1)-\sqrt{201}}{2*-2}=\frac{-1-\sqrt{201}}{-4}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{201}}{2*-2}=\frac{-1+\sqrt{201}}{-4}
$