116-2x^2=x^2+33x+5

Solution for 116-2x^2=x^2+33x+5 equation:

116-2x^2=x^2+33x+5

We move all terms to the left:

116-2x^2-(x^2+33x+5)=0

We get rid of parentheses

-2x^2-x^2-33x-5+116=0

We add all the numbers together, and all the variables

-3x^2-33x+111=0

a = -3; b = -33; c = +111;
Δ = b2-4ac
Δ = -332-4·(-3)·111
Δ = 2421
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:

$\sqrt{\Delta}=\sqrt{2421}=\sqrt{9*269}=\sqrt{9}*\sqrt{269}=3\sqrt{269}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{269}}{2*-3}=\frac{33-3\sqrt{269}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{269}}{2*-3}=\frac{33+3\sqrt{269}}{-6}
$