-4v2+120v=-188

Solution for -4v2+120v=-188 equation:

-4v^2+120v=-188

We move all terms to the left:

-4v^2+120v-(-188)=0

We add all the numbers together, and all the variables

-4v^2+120v+188=0

a = -4; b = 120; c = +188;
Δ = b2-4ac
Δ = 1202-4·(-4)·188
Δ = 17408
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:

$\sqrt{\Delta}=\sqrt{17408}=\sqrt{1024*17}=\sqrt{1024}*\sqrt{17}=32\sqrt{17}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-32\sqrt{17}}{2*-4}=\frac{-120-32\sqrt{17}}{-8}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+32\sqrt{17}}{2*-4}=\frac{-120+32\sqrt{17}}{-8}
$