9x^2+54x=22

Solution for 9x^2+54x=22 equation:

9x^2+54x=22

We move all terms to the left:

9x^2+54x-(22)=0

a = 9; b = 54; c = -22;
Δ = b2-4ac
Δ = 542-4·9·(-22)
Δ = 3708
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:

$\sqrt{\Delta}=\sqrt{3708}=\sqrt{36*103}=\sqrt{36}*\sqrt{103}=6\sqrt{103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{103}}{2*9}=\frac{-54-6\sqrt{103}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{103}}{2*9}=\frac{-54+6\sqrt{103}}{18}
$