9x(x-4)=45

Solution for 9x(x-4)=45 equation:

9x(x-4)=45

We move all terms to the left:

9x(x-4)-(45)=0

We multiply parentheses

9x^2-36x-45=0

a = 9; b = -36; c = -45;
Δ = b2-4ac
Δ = -362-4·9·(-45)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-54}{2*9}=\frac{-18}{18}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+54}{2*9}=\frac{90}{18}
=5
$