91-x^2=10

Solution for 91-x^2=10 equation:

91-x^2=10

We move all terms to the left:

91-x^2-(10)=0

We add all the numbers together, and all the variables

-1x^2+81=0

a = -1; b = 0; c = +81;
Δ = b2-4ac
Δ = 02-4·(-1)·81
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18}{2*-1}=\frac{18}{-2}
=-9
$