(4v-2)(2v-4)=90

Solution for (4v-2)(2v-4)=90 equation:

(4v-2)(2v-4)=90

We move all terms to the left:

(4v-2)(2v-4)-(90)=0

We multiply parentheses ..

(+8v^2-16v-4v+8)-90=0

We get rid of parentheses

8v^2-16v-4v+8-90=0

We add all the numbers together, and all the variables

8v^2-20v-82=0

a = 8; b = -20; c = -82;
Δ = b2-4ac
Δ = -202-4·8·(-82)
Δ = 3024
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:

$\sqrt{\Delta}=\sqrt{3024}=\sqrt{144*21}=\sqrt{144}*\sqrt{21}=12\sqrt{21}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-12\sqrt{21}}{2*8}=\frac{20-12\sqrt{21}}{16}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+12\sqrt{21}}{2*8}=\frac{20+12\sqrt{21}}{16}
$