10-2x^2=-198

Solution for 10-2x^2=-198 equation:

10-2x^2=-198

We move all terms to the left:

10-2x^2-(-198)=0

We add all the numbers together, and all the variables

-2x^2+208=0

a = -2; b = 0; c = +208;
Δ = b2-4ac
Δ = 02-4·(-2)·208
Δ = 1664
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:

$\sqrt{\Delta}=\sqrt{1664}=\sqrt{64*26}=\sqrt{64}*\sqrt{26}=8\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{26}}{2*-2}=\frac{0-8\sqrt{26}}{-4}
=-\frac{8\sqrt{26}}{-4}
=-\frac{2\sqrt{26}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{26}}{2*-2}=\frac{0+8\sqrt{26}}{-4}
=\frac{8\sqrt{26}}{-4}
=\frac{2\sqrt{26}}{-1}
$