-98=53-x^2

Solution for -98=53-x^2 equation:

-98=53-x^2

We move all terms to the left:

-98-(53-x^2)=0

We get rid of parentheses

x^2-53-98=0

We add all the numbers together, and all the variables

x^2-151=0

a = 1; b = 0; c = -151;
Δ = b2-4ac
Δ = 02-4·1·(-151)
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{151}}{2*1}=\frac{0-2\sqrt{151}}{2}
=-\frac{2\sqrt{151}}{2}
=-\sqrt{151}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{151}}{2*1}=\frac{0+2\sqrt{151}}{2}
=\frac{2\sqrt{151}}{2}
=\sqrt{151}
$