6x^2=36x-30

Solution for 6x^2=36x-30 equation:

6x^2=36x-30

We move all terms to the left:

6x^2-(36x-30)=0

We get rid of parentheses

6x^2-36x+30=0

a = 6; b = -36; c = +30;
Δ = b2-4ac
Δ = -362-4·6·30
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-24}{2*6}=\frac{12}{12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+24}{2*6}=\frac{60}{12}
=5
$