6x^2+60=18x^2-36x

Solution for 6x^2+60=18x^2-36x equation:

6x^2+60=18x^2-36x

We move all terms to the left:

6x^2+60-(18x^2-36x)=0

We get rid of parentheses

6x^2-18x^2+36x+60=0

We add all the numbers together, and all the variables

-12x^2+36x+60=0

a = -12; b = 36; c = +60;
Δ = b2-4ac
Δ = 362-4·(-12)·60
Δ = 4176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4176}=\sqrt{144*29}=\sqrt{144}*\sqrt{29}=12\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{29}}{2*-12}=\frac{-36-12\sqrt{29}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{29}}{2*-12}=\frac{-36+12\sqrt{29}}{-24}
$