(2x+10)(4x+30)=180

Solution for (2x+10)(4x+30)=180 equation:

(2x+10)(4x+30)=180

We move all terms to the left:

(2x+10)(4x+30)-(180)=0

We multiply parentheses ..

(+8x^2+60x+40x+300)-180=0

We get rid of parentheses

8x^2+60x+40x+300-180=0

We add all the numbers together, and all the variables

8x^2+100x+120=0

a = 8; b = 100; c = +120;
Δ = b2-4ac
Δ = 1002-4·8·120
Δ = 6160
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:

$\sqrt{\Delta}=\sqrt{6160}=\sqrt{16*385}=\sqrt{16}*\sqrt{385}=4\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{385}}{2*8}=\frac{-100-4\sqrt{385}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{385}}{2*8}=\frac{-100+4\sqrt{385}}{16}
$