(2x+2)(3x+8)=180

Solution for (2x+2)(3x+8)=180 equation:

(2x+2)(3x+8)=180

We move all terms to the left:

(2x+2)(3x+8)-(180)=0

We multiply parentheses ..

(+6x^2+16x+6x+16)-180=0

We get rid of parentheses

6x^2+16x+6x+16-180=0

We add all the numbers together, and all the variables

6x^2+22x-164=0

a = 6; b = 22; c = -164;
Δ = b2-4ac
Δ = 222-4·6·(-164)
Δ = 4420
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:

$\sqrt{\Delta}=\sqrt{4420}=\sqrt{4*1105}=\sqrt{4}*\sqrt{1105}=2\sqrt{1105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{1105}}{2*6}=\frac{-22-2\sqrt{1105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{1105}}{2*6}=\frac{-22+2\sqrt{1105}}{12}
$