9x(x+4)=18

Solution for 9x(x+4)=18 equation:

9x(x+4)=18

We move all terms to the left:

9x(x+4)-(18)=0

We multiply parentheses

9x^2+36x-18=0

a = 9; b = 36; c = -18;
Δ = b2-4ac
Δ = 362-4·9·(-18)
Δ = 1944
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:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-18\sqrt{6}}{2*9}=\frac{-36-18\sqrt{6}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+18\sqrt{6}}{2*9}=\frac{-36+18\sqrt{6}}{18}
$