2-4x2=-110

Solution for 2-4x2=-110 equation:

2-4x^2=-110

We move all terms to the left:

2-4x^2-(-110)=0

We add all the numbers together, and all the variables

-4x^2+112=0

a = -4; b = 0; c = +112;
Δ = b2-4ac
Δ = 02-4·(-4)·112
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{7}}{2*-4}=\frac{0-16\sqrt{7}}{-8}
=-\frac{16\sqrt{7}}{-8}
=-\frac{2\sqrt{7}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{7}}{2*-4}=\frac{0+16\sqrt{7}}{-8}
=\frac{16\sqrt{7}}{-8}
=\frac{2\sqrt{7}}{-1}
$