5x^2+12x^2=52^2

Solution for 5x^2+12x^2=52^2 equation:

5x^2+12x^2=52^2

We move all terms to the left:

5x^2+12x^2-(52^2)=0

We add all the numbers together, and all the variables

17x^2-2704=0

a = 17; b = 0; c = -2704;
Δ = b2-4ac
Δ = 02-4·17·(-2704)
Δ = 183872
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:

$\sqrt{\Delta}=\sqrt{183872}=\sqrt{10816*17}=\sqrt{10816}*\sqrt{17}=104\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-104\sqrt{17}}{2*17}=\frac{0-104\sqrt{17}}{34}
=-\frac{104\sqrt{17}}{34}
=-\frac{52\sqrt{17}}{17}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+104\sqrt{17}}{2*17}=\frac{0+104\sqrt{17}}{34}
=\frac{104\sqrt{17}}{34}
=\frac{52\sqrt{17}}{17}
$