5x^2+12x^2=24336

Solution for 5x^2+12x^2=24336 equation:

5x^2+12x^2=24336

We move all terms to the left:

5x^2+12x^2-(24336)=0

We add all the numbers together, and all the variables

17x^2-24336=0

a = 17; b = 0; c = -24336;
Δ = b2-4ac
Δ = 02-4·17·(-24336)
Δ = 1654848
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:

$\sqrt{\Delta}=\sqrt{1654848}=\sqrt{97344*17}=\sqrt{97344}*\sqrt{17}=312\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-312\sqrt{17}}{2*17}=\frac{0-312\sqrt{17}}{34}
=-\frac{312\sqrt{17}}{34}
=-\frac{156\sqrt{17}}{17}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+312\sqrt{17}}{2*17}=\frac{0+312\sqrt{17}}{34}
=\frac{312\sqrt{17}}{34}
=\frac{156\sqrt{17}}{17}
$