5x^2+3x^2=72^2

Solution for 5x^2+3x^2=72^2 equation:

5x^2+3x^2=72^2

We move all terms to the left:

5x^2+3x^2-(72^2)=0

We add all the numbers together, and all the variables

8x^2-5184=0

a = 8; b = 0; c = -5184;
Δ = b2-4ac
Δ = 02-4·8·(-5184)
Δ = 165888
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:

$\sqrt{\Delta}=\sqrt{165888}=\sqrt{82944*2}=\sqrt{82944}*\sqrt{2}=288\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-288\sqrt{2}}{2*8}=\frac{0-288\sqrt{2}}{16}
=-\frac{288\sqrt{2}}{16}
=-18\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+288\sqrt{2}}{2*8}=\frac{0+288\sqrt{2}}{16}
=\frac{288\sqrt{2}}{16}
=18\sqrt{2}
$