26x^2=2500

Solution for 26x^2=2500 equation:

26x^2=2500

We move all terms to the left:

26x^2-(2500)=0

a = 26; b = 0; c = -2500;
Δ = b2-4ac
Δ = 02-4·26·(-2500)
Δ = 260000
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:

$\sqrt{\Delta}=\sqrt{260000}=\sqrt{10000*26}=\sqrt{10000}*\sqrt{26}=100\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{26}}{2*26}=\frac{0-100\sqrt{26}}{52}
=-\frac{100\sqrt{26}}{52}
=-\frac{25\sqrt{26}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{26}}{2*26}=\frac{0+100\sqrt{26}}{52}
=\frac{100\sqrt{26}}{52}
=\frac{25\sqrt{26}}{13}
$