9x^2-116-18x=0

Solution for 9x^2-116-18x=0 equation:

9x^2-116-18x=0

a = 9; b = -18; c = -116;
Δ = b2-4ac
Δ = -182-4·9·(-116)
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-30\sqrt{5}}{2*9}=\frac{18-30\sqrt{5}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+30\sqrt{5}}{2*9}=\frac{18+30\sqrt{5}}{18}
$