x+7=x^2+6x+11

Solution for x+7=x^2+6x+11 equation:

x+7=x^2+6x+11

We move all terms to the left:

x+7-(x^2+6x+11)=0

We get rid of parentheses

-x^2+x-6x-11+7=0

We add all the numbers together, and all the variables

-1x^2-5x-4=0

a = -1; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·(-1)·(-4)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*-1}=\frac{2}{-2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*-1}=\frac{8}{-2}
=-4
$