19-2x^2=-98

Solution for 19-2x^2=-98 equation:

19-2x^2=-98

We move all terms to the left:

19-2x^2-(-98)=0

We add all the numbers together, and all the variables

-2x^2+117=0

a = -2; b = 0; c = +117;
Δ = b2-4ac
Δ = 02-4·(-2)·117
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{26}}{2*-2}=\frac{0-6\sqrt{26}}{-4}
=-\frac{6\sqrt{26}}{-4}
=-\frac{3\sqrt{26}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{26}}{2*-2}=\frac{0+6\sqrt{26}}{-4}
=\frac{6\sqrt{26}}{-4}
=\frac{3\sqrt{26}}{-2}
$