4x^2-20x^2=-24

Solution for 4x^2-20x^2=-24 equation:

4x^2-20x^2=-24

We move all terms to the left:

4x^2-20x^2-(-24)=0

We add all the numbers together, and all the variables

-16x^2+24=0

a = -16; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-16)·24
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{6}}{2*-16}=\frac{0-16\sqrt{6}}{-32}
=-\frac{16\sqrt{6}}{-32}
=-\frac{\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{6}}{2*-16}=\frac{0+16\sqrt{6}}{-32}
=\frac{16\sqrt{6}}{-32}
=\frac{\sqrt{6}}{-2}
$