x+33=x^2+10

Solution for x+33=x^2+10 equation:

x+33=x^2+10

We move all terms to the left:

x+33-(x^2+10)=0

We get rid of parentheses

-x^2+x-10+33=0

We add all the numbers together, and all the variables

-1x^2+x+23=0

a = -1; b = 1; c = +23;
Δ = b2-4ac
Δ = 12-4·(-1)·23
Δ = 93
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{93}}{2*-1}=\frac{-1-\sqrt{93}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{93}}{2*-1}=\frac{-1+\sqrt{93}}{-2}
$