30+13v(v+24)=180

Solution for 30+13v(v+24)=180 equation:

30+13v(v+24)=180

We move all terms to the left:

30+13v(v+24)-(180)=0

We add all the numbers together, and all the variables

13v(v+24)-150=0

We multiply parentheses

13v^2+312v-150=0

a = 13; b = 312; c = -150;
Δ = b2-4ac
Δ = 3122-4·13·(-150)
Δ = 105144
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:

$\sqrt{\Delta}=\sqrt{105144}=\sqrt{4*26286}=\sqrt{4}*\sqrt{26286}=2\sqrt{26286}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(312)-2\sqrt{26286}}{2*13}=\frac{-312-2\sqrt{26286}}{26}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(312)+2\sqrt{26286}}{2*13}=\frac{-312+2\sqrt{26286}}{26}
$