(9x-6)(x+16)=180

Solution for (9x-6)(x+16)=180 equation:

(9x-6)(x+16)=180

We move all terms to the left:

(9x-6)(x+16)-(180)=0

We multiply parentheses ..

(+9x^2+144x-6x-96)-180=0

We get rid of parentheses

9x^2+144x-6x-96-180=0

We add all the numbers together, and all the variables

9x^2+138x-276=0

a = 9; b = 138; c = -276;
Δ = b2-4ac
Δ = 1382-4·9·(-276)
Δ = 28980
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28980}=\sqrt{36*805}=\sqrt{36}*\sqrt{805}=6\sqrt{805}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(138)-6\sqrt{805}}{2*9}=\frac{-138-6\sqrt{805}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(138)+6\sqrt{805}}{2*9}=\frac{-138+6\sqrt{805}}{18}
$