50x^2+x^2=60^2

Solution for 50x^2+x^2=60^2 equation:

50x^2+x^2=60^2

We move all terms to the left:

50x^2+x^2-(60^2)=0

We add all the numbers together, and all the variables

51x^2-3600=0

a = 51; b = 0; c = -3600;
Δ = b2-4ac
Δ = 02-4·51·(-3600)
Δ = 734400
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:

$\sqrt{\Delta}=\sqrt{734400}=\sqrt{14400*51}=\sqrt{14400}*\sqrt{51}=120\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120\sqrt{51}}{2*51}=\frac{0-120\sqrt{51}}{102}
=-\frac{120\sqrt{51}}{102}
=-\frac{20\sqrt{51}}{17}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120\sqrt{51}}{2*51}=\frac{0+120\sqrt{51}}{102}
=\frac{120\sqrt{51}}{102}
=\frac{20\sqrt{51}}{17}
$