24x^2+7x^2=100^2

Solution for 24x^2+7x^2=100^2 equation:

24x^2+7x^2=100^2

We move all terms to the left:

24x^2+7x^2-(100^2)=0

We add all the numbers together, and all the variables

31x^2-10000=0

a = 31; b = 0; c = -10000;
Δ = b2-4ac
Δ = 02-4·31·(-10000)
Δ = 1240000
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:

$\sqrt{\Delta}=\sqrt{1240000}=\sqrt{40000*31}=\sqrt{40000}*\sqrt{31}=200\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{31}}{2*31}=\frac{0-200\sqrt{31}}{62}
=-\frac{200\sqrt{31}}{62}
=-\frac{100\sqrt{31}}{31}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{31}}{2*31}=\frac{0+200\sqrt{31}}{62}
=\frac{200\sqrt{31}}{62}
=\frac{100\sqrt{31}}{31}
$