10+x=11x+x^2+7

Solution for 10+x=11x+x^2+7 equation:

10+x=11x+x^2+7

We move all terms to the left:

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

We get rid of parentheses

-x^2-11x+x-7+10=0

We add all the numbers together, and all the variables

-1x^2-10x+3=0

a = -1; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·(-1)·3
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{7}}{2*-1}=\frac{10-4\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{7}}{2*-1}=\frac{10+4\sqrt{7}}{-2}
$