(2x+10)(5x+30)=180

Solution for (2x+10)(5x+30)=180 equation:

(2x+10)(5x+30)=180

We move all terms to the left:

(2x+10)(5x+30)-(180)=0

We multiply parentheses ..

(+10x^2+60x+50x+300)-180=0

We get rid of parentheses

10x^2+60x+50x+300-180=0

We add all the numbers together, and all the variables

10x^2+110x+120=0

a = 10; b = 110; c = +120;
Δ = b2-4ac
Δ = 1102-4·10·120
Δ = 7300
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:

$\sqrt{\Delta}=\sqrt{7300}=\sqrt{100*73}=\sqrt{100}*\sqrt{73}=10\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-10\sqrt{73}}{2*10}=\frac{-110-10\sqrt{73}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+10\sqrt{73}}{2*10}=\frac{-110+10\sqrt{73}}{20}
$