(2x+6)(8x+4)=180

Solution for (2x+6)(8x+4)=180 equation:

(2x+6)(8x+4)=180

We move all terms to the left:

(2x+6)(8x+4)-(180)=0

We multiply parentheses ..

(+16x^2+8x+48x+24)-180=0

We get rid of parentheses

16x^2+8x+48x+24-180=0

We add all the numbers together, and all the variables

16x^2+56x-156=0

a = 16; b = 56; c = -156;
Δ = b2-4ac
Δ = 562-4·16·(-156)
Δ = 13120
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:

$\sqrt{\Delta}=\sqrt{13120}=\sqrt{64*205}=\sqrt{64}*\sqrt{205}=8\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-8\sqrt{205}}{2*16}=\frac{-56-8\sqrt{205}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+8\sqrt{205}}{2*16}=\frac{-56+8\sqrt{205}}{32}
$