180=x(x+15)+39

Solution for 180=x(x+15)+39 equation:

180=x(x+15)+39

We move all terms to the left:

180-(x(x+15)+39)=0


We calculate terms in parentheses: -(x(x+15)+39), so:

x(x+15)+39

We multiply parentheses

x^2+15x+39

Back to the equation:

-(x^2+15x+39)


We get rid of parentheses

-x^2-15x-39+180=0

We add all the numbers together, and all the variables

-1x^2-15x+141=0

a = -1; b = -15; c = +141;
Δ = b2-4ac
Δ = -152-4·(-1)·141
Δ = 789
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{-(-15)-\sqrt{789}}{2*-1}=\frac{15-\sqrt{789}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{789}}{2*-1}=\frac{15+\sqrt{789}}{-2}
$