(2x+10)(4x+20)=180

Solution for (2x+10)(4x+20)=180 equation:

(2x+10)(4x+20)=180

We move all terms to the left:

(2x+10)(4x+20)-(180)=0

We multiply parentheses ..

(+8x^2+40x+40x+200)-180=0

We get rid of parentheses

8x^2+40x+40x+200-180=0

We add all the numbers together, and all the variables

8x^2+80x+20=0

a = 8; b = 80; c = +20;
Δ = b2-4ac
Δ = 802-4·8·20
Δ = 5760
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:

$\sqrt{\Delta}=\sqrt{5760}=\sqrt{576*10}=\sqrt{576}*\sqrt{10}=24\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-24\sqrt{10}}{2*8}=\frac{-80-24\sqrt{10}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+24\sqrt{10}}{2*8}=\frac{-80+24\sqrt{10}}{16}
$