x^2-4=-4x^2+1124

Solution for x^2-4=-4x^2+1124 equation:

x^2-4=-4x^2+1124

We move all terms to the left:

x^2-4-(-4x^2+1124)=0

We get rid of parentheses

x^2+4x^2-1124-4=0

We add all the numbers together, and all the variables

5x^2-1128=0

a = 5; b = 0; c = -1128;
Δ = b2-4ac
Δ = 02-4·5·(-1128)
Δ = 22560
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:

$\sqrt{\Delta}=\sqrt{22560}=\sqrt{16*1410}=\sqrt{16}*\sqrt{1410}=4\sqrt{1410}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{1410}}{2*5}=\frac{0-4\sqrt{1410}}{10}
=-\frac{4\sqrt{1410}}{10}
=-\frac{2\sqrt{1410}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{1410}}{2*5}=\frac{0+4\sqrt{1410}}{10}
=\frac{4\sqrt{1410}}{10}
=\frac{2\sqrt{1410}}{5}
$