11-3x=x^2-2x-3

Solution for 11-3x=x^2-2x-3 equation:

11-3x=x^2-2x-3

We move all terms to the left:

11-3x-(x^2-2x-3)=0

We get rid of parentheses

-x^2-3x+2x+3+11=0

We add all the numbers together, and all the variables

-1x^2-1x+14=0

a = -1; b = -1; c = +14;
Δ = b2-4ac
Δ = -12-4·(-1)·14
Δ = 57
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{57}}{2*-1}=\frac{1-\sqrt{57}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{57}}{2*-1}=\frac{1+\sqrt{57}}{-2}
$