4v^2-8v-145=-5

Solution for 4v^2-8v-145=-5 equation:

4v^2-8v-145=-5

We move all terms to the left:

4v^2-8v-145-(-5)=0

We add all the numbers together, and all the variables

4v^2-8v-140=0

a = 4; b = -8; c = -140;
Δ = b2-4ac
Δ = -82-4·4·(-140)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-48}{2*4}=\frac{-40}{8}
=-5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+48}{2*4}=\frac{56}{8}
=7
$