60-6x^2=3x^2

Solution for 60-6x^2=3x^2 equation:

60-6x^2=3x^2

We move all terms to the left:

60-6x^2-(3x^2)=0

We add all the numbers together, and all the variables

-9x^2+60=0

a = -9; b = 0; c = +60;
Δ = b2-4ac
Δ = 02-4·(-9)·60
Δ = 2160
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:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{15}}{2*-9}=\frac{0-12\sqrt{15}}{-18}
=-\frac{12\sqrt{15}}{-18}
=-\frac{2\sqrt{15}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{15}}{2*-9}=\frac{0+12\sqrt{15}}{-18}
=\frac{12\sqrt{15}}{-18}
=\frac{2\sqrt{15}}{-3}
$