X^2-8x^2+24=0

Solution for X^2-8x^2+24=0 equation:

X^2-8X^2+24=0

We add all the numbers together, and all the variables

-7X^2+24=0

a = -7; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-7)·24
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{42}}{2*-7}=\frac{0-4\sqrt{42}}{-14}
=-\frac{4\sqrt{42}}{-14}
=-\frac{2\sqrt{42}}{-7}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42}}{2*-7}=\frac{0+4\sqrt{42}}{-14}
=\frac{4\sqrt{42}}{-14}
=\frac{2\sqrt{42}}{-7}
$