180=3x(x+15)+43

Solution for 180=3x(x+15)+43 equation:

180=3x(x+15)+43

We move all terms to the left:

180-(3x(x+15)+43)=0


We calculate terms in parentheses: -(3x(x+15)+43), so:

3x(x+15)+43

We multiply parentheses

3x^2+45x+43

Back to the equation:

-(3x^2+45x+43)


We get rid of parentheses

-3x^2-45x-43+180=0

We add all the numbers together, and all the variables

-3x^2-45x+137=0

a = -3; b = -45; c = +137;
Δ = b2-4ac
Δ = -452-4·(-3)·137
Δ = 3669
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{-(-45)-\sqrt{3669}}{2*-3}=\frac{45-\sqrt{3669}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{3669}}{2*-3}=\frac{45+\sqrt{3669}}{-6}
$