5^2=6x^2

Solution for 5^2=6x^2 equation:

5^2=6x^2

We move all terms to the left:

5^2-(6x^2)=0

We add all the numbers together, and all the variables

-6x^2+25=0

a = -6; b = 0; c = +25;
Δ = b2-4ac
Δ = 02-4·(-6)·25
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*-6}=\frac{0-10\sqrt{6}}{-12}
=-\frac{10\sqrt{6}}{-12}
=-\frac{5\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*-6}=\frac{0+10\sqrt{6}}{-12}
=\frac{10\sqrt{6}}{-12}
=\frac{5\sqrt{6}}{-6}
$