9x^2=11+18x

Solution for 9x^2=11+18x equation:

9x^2=11+18x

We move all terms to the left:

9x^2-(11+18x)=0

We add all the numbers together, and all the variables

9x^2-(18x+11)=0

We get rid of parentheses

9x^2-18x-11=0

a = 9; b = -18; c = -11;
Δ = b2-4ac
Δ = -182-4·9·(-11)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-12\sqrt{5}}{2*9}=\frac{18-12\sqrt{5}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12\sqrt{5}}{2*9}=\frac{18+12\sqrt{5}}{18}
$