52x2=125

Solution for 52x2=125 equation:

52x^2=125

We move all terms to the left:

52x^2-(125)=0

a = 52; b = 0; c = -125;
Δ = b2-4ac
Δ = 02-4·52·(-125)
Δ = 26000
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:

$\sqrt{\Delta}=\sqrt{26000}=\sqrt{400*65}=\sqrt{400}*\sqrt{65}=20\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{65}}{2*52}=\frac{0-20\sqrt{65}}{104}
=-\frac{20\sqrt{65}}{104}
=-\frac{5\sqrt{65}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{65}}{2*52}=\frac{0+20\sqrt{65}}{104}
=\frac{20\sqrt{65}}{104}
=\frac{5\sqrt{65}}{26}
$