(v+15)+8v(v+15)=180

Solution for (v+15)+8v(v+15)=180 equation:

(v+15)+8v(v+15)=180

We move all terms to the left:

(v+15)+8v(v+15)-(180)=0

We multiply parentheses

8v^2+(v+15)+120v-180=0

We get rid of parentheses

8v^2+v+120v+15-180=0

We add all the numbers together, and all the variables

8v^2+121v-165=0

a = 8; b = 121; c = -165;
Δ = b2-4ac
Δ = 1212-4·8·(-165)
Δ = 19921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(121)-\sqrt{19921}}{2*8}=\frac{-121-\sqrt{19921}}{16}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(121)+\sqrt{19921}}{2*8}=\frac{-121+\sqrt{19921}}{16}
$