v^2+8v-101=-9

Solution for v^2+8v-101=-9 equation:

v^2+8v-101=-9

We move all terms to the left:

v^2+8v-101-(-9)=0

We add all the numbers together, and all the variables

v^2+8v-92=0

a = 1; b = 8; c = -92;
Δ = b2-4ac
Δ = 82-4·1·(-92)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12\sqrt{3}}{2*1}=\frac{-8-12\sqrt{3}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12\sqrt{3}}{2*1}=\frac{-8+12\sqrt{3}}{2}
$