24=4+37x^2-16x^2

Solution for 24=4+37x^2-16x^2 equation:

24=4+37x^2-16x^2

We move all terms to the left:

24-(4+37x^2-16x^2)=0

We get rid of parentheses

-37x^2+16x^2-4+24=0

We add all the numbers together, and all the variables

-21x^2+20=0

a = -21; b = 0; c = +20;
Δ = b2-4ac
Δ = 02-4·(-21)·20
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{105}}{2*-21}=\frac{0-4\sqrt{105}}{-42}
=-\frac{4\sqrt{105}}{-42}
=-\frac{2\sqrt{105}}{-21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{105}}{2*-21}=\frac{0+4\sqrt{105}}{-42}
=\frac{4\sqrt{105}}{-42}
=\frac{2\sqrt{105}}{-21}
$