4x^2+x^2=25^2

Solution for 4x^2+x^2=25^2 equation:

4x^2+x^2=25^2

We move all terms to the left:

4x^2+x^2-(25^2)=0

We add all the numbers together, and all the variables

5x^2-625=0

a = 5; b = 0; c = -625;
Δ = b2-4ac
Δ = 02-4·5·(-625)
Δ = 12500
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:

$\sqrt{\Delta}=\sqrt{12500}=\sqrt{2500*5}=\sqrt{2500}*\sqrt{5}=50\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50\sqrt{5}}{2*5}=\frac{0-50\sqrt{5}}{10}
=-\frac{50\sqrt{5}}{10}
=-5\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50\sqrt{5}}{2*5}=\frac{0+50\sqrt{5}}{10}
=\frac{50\sqrt{5}}{10}
=5\sqrt{5}
$