5x(6x-9)=5x

Solution for 5x(6x-9)=5x equation:

5x(6x-9)=5x

We move all terms to the left:

5x(6x-9)-(5x)=0

We add all the numbers together, and all the variables

-5x+5x(6x-9)=0

We multiply parentheses

30x^2-5x-45x=0

We add all the numbers together, and all the variables

30x^2-50x=0

a = 30; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·30·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*30}=\frac{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*30}=\frac{100}{60}
=1+2/3
$