9x(x-5)=108

Solution for 9x(x-5)=108 equation:

9x(x-5)=108

We move all terms to the left:

9x(x-5)-(108)=0

We multiply parentheses

9x^2-45x-108=0

a = 9; b = -45; c = -108;
Δ = b2-4ac
Δ = -452-4·9·(-108)
Δ = 5913
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:

$\sqrt{\Delta}=\sqrt{5913}=\sqrt{81*73}=\sqrt{81}*\sqrt{73}=9\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-9\sqrt{73}}{2*9}=\frac{45-9\sqrt{73}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+9\sqrt{73}}{2*9}=\frac{45+9\sqrt{73}}{18}
$