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

Solution for X^2+12x^2-60=0 equation:

X^2+12X^2-60=0

We add all the numbers together, and all the variables

13X^2-60=0

a = 13; b = 0; c = -60;
Δ = b2-4ac
Δ = 02-4·13·(-60)
Δ = 3120
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:

$\sqrt{\Delta}=\sqrt{3120}=\sqrt{16*195}=\sqrt{16}*\sqrt{195}=4\sqrt{195}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{195}}{2*13}=\frac{0-4\sqrt{195}}{26}
=-\frac{4\sqrt{195}}{26}
=-\frac{2\sqrt{195}}{13}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{195}}{2*13}=\frac{0+4\sqrt{195}}{26}
=\frac{4\sqrt{195}}{26}
=\frac{2\sqrt{195}}{13}
$