18=2(x+3)x=

Solution for 18=2(x+3)x= equation:

18=2(x+3)x=

We move all terms to the left:

18-(2(x+3)x)=0


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

2(x+3)x

We multiply parentheses

2x^2+6x

Back to the equation:

-(2x^2+6x)


We get rid of parentheses

-2x^2-6x+18=0

a = -2; b = -6; c = +18;
Δ = b2-4ac
Δ = -62-4·(-2)·18
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{5}}{2*-2}=\frac{6-6\sqrt{5}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{5}}{2*-2}=\frac{6+6\sqrt{5}}{-4}
$