12x^2+5x^2=75^2

Solution for 12x^2+5x^2=75^2 equation:

12x^2+5x^2=75^2

We move all terms to the left:

12x^2+5x^2-(75^2)=0

We add all the numbers together, and all the variables

17x^2-5625=0

a = 17; b = 0; c = -5625;
Δ = b2-4ac
Δ = 02-4·17·(-5625)
Δ = 382500
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:

$\sqrt{\Delta}=\sqrt{382500}=\sqrt{22500*17}=\sqrt{22500}*\sqrt{17}=150\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-150\sqrt{17}}{2*17}=\frac{0-150\sqrt{17}}{34}
=-\frac{150\sqrt{17}}{34}
=-\frac{75\sqrt{17}}{17}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+150\sqrt{17}}{2*17}=\frac{0+150\sqrt{17}}{34}
=\frac{150\sqrt{17}}{34}
=\frac{75\sqrt{17}}{17}
$