180=x(2x+21)

Solution for 180=x(2x+21) equation:

180=x(2x+21)

We move all terms to the left:

180-(x(2x+21))=0


We calculate terms in parentheses: -(x(2x+21)), so:

x(2x+21)

We multiply parentheses

2x^2+21x

Back to the equation:

-(2x^2+21x)


We get rid of parentheses

-2x^2-21x+180=0

a = -2; b = -21; c = +180;
Δ = b2-4ac
Δ = -212-4·(-2)·180
Δ = 1881
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:

$\sqrt{\Delta}=\sqrt{1881}=\sqrt{9*209}=\sqrt{9}*\sqrt{209}=3\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{209}}{2*-2}=\frac{21-3\sqrt{209}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{209}}{2*-2}=\frac{21+3\sqrt{209}}{-4}
$