(4v+38)(9v+77)=180

Solution for (4v+38)(9v+77)=180 equation:

(4v+38)(9v+77)=180

We move all terms to the left:

(4v+38)(9v+77)-(180)=0

We multiply parentheses ..

(+36v^2+308v+342v+2926)-180=0

We get rid of parentheses

36v^2+308v+342v+2926-180=0

We add all the numbers together, and all the variables

36v^2+650v+2746=0

a = 36; b = 650; c = +2746;
Δ = b2-4ac
Δ = 6502-4·36·2746
Δ = 27076
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:

$\sqrt{\Delta}=\sqrt{27076}=\sqrt{4*6769}=\sqrt{4}*\sqrt{6769}=2\sqrt{6769}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(650)-2\sqrt{6769}}{2*36}=\frac{-650-2\sqrt{6769}}{72}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(650)+2\sqrt{6769}}{2*36}=\frac{-650+2\sqrt{6769}}{72}
$