11x=x^2-33.75

Solution for 11x=x^2-33.75 equation:

11x=x^2-33.75

We move all terms to the left:

11x-(x^2-33.75)=0

We get rid of parentheses

-x^2+11x+33.75=0

We add all the numbers together, and all the variables

-1x^2+11x+33.75=0

a = -1; b = 11; c = +33.75;
Δ = b2-4ac
Δ = 112-4·(-1)·33.75
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-16}{2*-1}=\frac{-27}{-2}
=13+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+16}{2*-1}=\frac{5}{-2}
=-2+1/2
$