62-x^2=4x^2

Solution for 62-x^2=4x^2 equation:

62-x^2=4x^2

We move all terms to the left:

62-x^2-(4x^2)=0

We add all the numbers together, and all the variables

-5x^2+62=0

a = -5; b = 0; c = +62;
Δ = b2-4ac
Δ = 02-4·(-5)·62
Δ = 1240
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:

$\sqrt{\Delta}=\sqrt{1240}=\sqrt{4*310}=\sqrt{4}*\sqrt{310}=2\sqrt{310}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{310}}{2*-5}=\frac{0-2\sqrt{310}}{-10}
=-\frac{2\sqrt{310}}{-10}
=-\frac{\sqrt{310}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{310}}{2*-5}=\frac{0+2\sqrt{310}}{-10}
=\frac{2\sqrt{310}}{-10}
=\frac{\sqrt{310}}{-5}
$