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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -((x+30)+x(5x+10)), so:

(x+30)+x(5x+10)

We multiply parentheses

5x^2+(x+30)+10x

We get rid of parentheses

5x^2+x+10x+30

We add all the numbers together, and all the variables

5x^2+11x+30

Back to the equation:

-(5x^2+11x+30)


We get rid of parentheses

-5x^2-11x-30+180=0

We add all the numbers together, and all the variables

-5x^2-11x+150=0

a = -5; b = -11; c = +150;
Δ = b2-4ac
Δ = -112-4·(-5)·150
Δ = 3121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{3121}}{2*-5}=\frac{11-\sqrt{3121}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{3121}}{2*-5}=\frac{11+\sqrt{3121}}{-10}
$