15v^2-v-121=8v^2-5

Solution for 15v^2-v-121=8v^2-5 equation:

15v^2-v-121=8v^2-5

We move all terms to the left:

15v^2-v-121-(8v^2-5)=0

We add all the numbers together, and all the variables

15v^2-1v-(8v^2-5)-121=0

We get rid of parentheses

15v^2-8v^2-1v+5-121=0

We add all the numbers together, and all the variables

7v^2-1v-116=0

a = 7; b = -1; c = -116;
Δ = b2-4ac
Δ = -12-4·7·(-116)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-57}{2*7}=\frac{-56}{14}
=-4
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+57}{2*7}=\frac{58}{14}
=4+1/7
$