5x(x-6)=5x-30

Solution for 5x(x-6)=5x-30 equation:

5x(x-6)=5x-30

We move all terms to the left:

5x(x-6)-(5x-30)=0

We multiply parentheses

5x^2-30x-(5x-30)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

5x^2-35x+30=0

a = 5; b = -35; c = +30;
Δ = b2-4ac
Δ = -352-4·5·30
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-25}{2*5}=\frac{10}{10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+25}{2*5}=\frac{60}{10}
=6
$