0=9(x2+6x)-18

Solution for 0=9(x2+6x)-18 equation:

0=9(x2+6x)-18

We move all terms to the left:

0-(9(x2+6x)-18)=0

We add all the numbers together, and all the variables

-(9(+x^2+6x)-18)+0=0

We add all the numbers together, and all the variables

-(9(+x^2+6x)-18)=0


We calculate terms in parentheses: -(9(+x^2+6x)-18), so:

9(+x^2+6x)-18

We multiply parentheses

9x^2+54x-18

Back to the equation:

-(9x^2+54x-18)


We get rid of parentheses

-9x^2-54x+18=0

a = -9; b = -54; c = +18;
Δ = b2-4ac
Δ = -542-4·(-9)·18
Δ = 3564
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:

$\sqrt{\Delta}=\sqrt{3564}=\sqrt{324*11}=\sqrt{324}*\sqrt{11}=18\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-18\sqrt{11}}{2*-9}=\frac{54-18\sqrt{11}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+18\sqrt{11}}{2*-9}=\frac{54+18\sqrt{11}}{-18}
$