180=(2x+45)(x)

Solution for 180=(2x+45)(x) equation:

180=(2x+45)(x)

We move all terms to the left:

180-((2x+45)(x))=0


We calculate terms in parentheses: -((2x+45)x), so:

(2x+45)x

We multiply parentheses

2x^2+45x

Back to the equation:

-(2x^2+45x)


We get rid of parentheses

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

a = -2; b = -45; c = +180;
Δ = b2-4ac
Δ = -452-4·(-2)·180
Δ = 3465
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:

$\sqrt{\Delta}=\sqrt{3465}=\sqrt{9*385}=\sqrt{9}*\sqrt{385}=3\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{385}}{2*-2}=\frac{45-3\sqrt{385}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{385}}{2*-2}=\frac{45+3\sqrt{385}}{-4}
$