180=(x+15+)(3x+10)+x

Solution for 180=(x+15+)(3x+10)+x equation:

180=(x+15+)(3x+10)+x

We move all terms to the left:

180-((x+15+)(3x+10)+x)=0

We add all the numbers together, and all the variables

-((+x)(3x+10)+x)+180=0

We multiply parentheses ..

-((+3x^2+10x)+x)+180=0


We calculate terms in parentheses: -((+3x^2+10x)+x), so:

(+3x^2+10x)+x

We get rid of parentheses

3x^2+10x+x

We add all the numbers together, and all the variables

3x^2+11x

Back to the equation:

-(3x^2+11x)


We get rid of parentheses

-3x^2-11x+180=0

a = -3; b = -11; c = +180;
Δ = b2-4ac
Δ = -112-4·(-3)·180
Δ = 2281
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{2281}}{2*-3}=\frac{11-\sqrt{2281}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{2281}}{2*-3}=\frac{11+\sqrt{2281}}{-6}
$