(2x+18)(6x+8)=180

Solution for (2x+18)(6x+8)=180 equation:

(2x+18)(6x+8)=180

We move all terms to the left:

(2x+18)(6x+8)-(180)=0

We multiply parentheses ..

(+12x^2+16x+108x+144)-180=0

We get rid of parentheses

12x^2+16x+108x+144-180=0

We add all the numbers together, and all the variables

12x^2+124x-36=0

a = 12; b = 124; c = -36;
Δ = b2-4ac
Δ = 1242-4·12·(-36)
Δ = 17104
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:

$\sqrt{\Delta}=\sqrt{17104}=\sqrt{16*1069}=\sqrt{16}*\sqrt{1069}=4\sqrt{1069}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(124)-4\sqrt{1069}}{2*12}=\frac{-124-4\sqrt{1069}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(124)+4\sqrt{1069}}{2*12}=\frac{-124+4\sqrt{1069}}{24}
$