(2v+8)(2v+8)=90

Solution for (2v+8)(2v+8)=90 equation:

(2v+8)(2v+8)=90

We move all terms to the left:

(2v+8)(2v+8)-(90)=0

We multiply parentheses ..

(+4v^2+16v+16v+64)-90=0

We get rid of parentheses

4v^2+16v+16v+64-90=0

We add all the numbers together, and all the variables

4v^2+32v-26=0

a = 4; b = 32; c = -26;
Δ = b2-4ac
Δ = 322-4·4·(-26)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-12\sqrt{10}}{2*4}=\frac{-32-12\sqrt{10}}{8}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+12\sqrt{10}}{2*4}=\frac{-32+12\sqrt{10}}{8}
$