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-150=0

a = 4; b = -8; c = -150;
Δ = b2-4ac
Δ = -82-4·4·(-150)
Δ = 2464
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:

$\sqrt{\Delta}=\sqrt{2464}=\sqrt{16*154}=\sqrt{16}*\sqrt{154}=4\sqrt{154}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{154}}{2*4}=\frac{8-4\sqrt{154}}{8}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{154}}{2*4}=\frac{8+4\sqrt{154}}{8}
$