2x^2-188=224

Solution for 2x^2-188=224 equation:

2x^2-188=224

We move all terms to the left:

2x^2-188-(224)=0

We add all the numbers together, and all the variables

2x^2-412=0

a = 2; b = 0; c = -412;
Δ = b2-4ac
Δ = 02-4·2·(-412)
Δ = 3296
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:

$\sqrt{\Delta}=\sqrt{3296}=\sqrt{16*206}=\sqrt{16}*\sqrt{206}=4\sqrt{206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{206}}{2*2}=\frac{0-4\sqrt{206}}{4}
=-\frac{4\sqrt{206}}{4}
=-\sqrt{206}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{206}}{2*2}=\frac{0+4\sqrt{206}}{4}
=\frac{4\sqrt{206}}{4}
=\sqrt{206}
$