x^2-10+x^2-98=188

Solution for x^2-10+x^2-98=188 equation:

x^2-10+x^2-98=188

We move all terms to the left:

x^2-10+x^2-98-(188)=0

We add all the numbers together, and all the variables

2x^2-296=0

a = 2; b = 0; c = -296;
Δ = b2-4ac
Δ = 02-4·2·(-296)
Δ = 2368
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:

$\sqrt{\Delta}=\sqrt{2368}=\sqrt{64*37}=\sqrt{64}*\sqrt{37}=8\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{37}}{2*2}=\frac{0-8\sqrt{37}}{4}
=-\frac{8\sqrt{37}}{4}
=-2\sqrt{37}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{37}}{2*2}=\frac{0+8\sqrt{37}}{4}
=\frac{8\sqrt{37}}{4}
=2\sqrt{37}
$