3x+11=x^2+2+1

Solution for 3x+11=x^2+2+1 equation:

3x+11=x^2+2+1

We move all terms to the left:

3x+11-(x^2+2+1)=0

We get rid of parentheses

-x^2+3x-2-1+11=0

We add all the numbers together, and all the variables

-1x^2+3x+8=0

a = -1; b = 3; c = +8;
Δ = b2-4ac
Δ = 32-4·(-1)·8
Δ = 41
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{-(3)-\sqrt{41}}{2*-1}=\frac{-3-\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{41}}{2*-1}=\frac{-3+\sqrt{41}}{-2}
$