25x^2=52

Solution for 25x^2=52 equation:

25x^2=52

We move all terms to the left:

25x^2-(52)=0

a = 25; b = 0; c = -52;
Δ = b2-4ac
Δ = 02-4·25·(-52)
Δ = 5200
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:

$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{13}}{2*25}=\frac{0-20\sqrt{13}}{50}
=-\frac{20\sqrt{13}}{50}
=-\frac{2\sqrt{13}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{13}}{2*25}=\frac{0+20\sqrt{13}}{50}
=\frac{20\sqrt{13}}{50}
=\frac{2\sqrt{13}}{5}
$