9x2+54x=18

Solution for 9x2+54x=18 equation:

9x^2+54x=18

We move all terms to the left:

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}
$