30x=5x(x-6)

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

30x=5x(x-6)

We move all terms to the left:

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


We calculate terms in parentheses: -(5x(x-6)), so:

5x(x-6)

We multiply parentheses

5x^2-30x

Back to the equation:

-(5x^2-30x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-5x^2+60x=0

a = -5; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-5)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-5}=\frac{-120}{-10}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-5}=\frac{0}{-10}
=0
$