(3x-9)(x+7)=180

Solution for (3x-9)(x+7)=180 equation:

(3x-9)(x+7)=180

We move all terms to the left:

(3x-9)(x+7)-(180)=0

We multiply parentheses ..

(+3x^2+21x-9x-63)-180=0

We get rid of parentheses

3x^2+21x-9x-63-180=0

We add all the numbers together, and all the variables

3x^2+12x-243=0

a = 3; b = 12; c = -243;
Δ = b2-4ac
Δ = 122-4·3·(-243)
Δ = 3060
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:

$\sqrt{\Delta}=\sqrt{3060}=\sqrt{36*85}=\sqrt{36}*\sqrt{85}=6\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{85}}{2*3}=\frac{-12-6\sqrt{85}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{85}}{2*3}=\frac{-12+6\sqrt{85}}{6}
$