143=2x+x^2

Solution for 143=2x+x^2 equation:

143=2x+x^2

We move all terms to the left:

143-(2x+x^2)=0

We get rid of parentheses

-x^2-2x+143=0

We add all the numbers together, and all the variables

-1x^2-2x+143=0

a = -1; b = -2; c = +143;
Δ = b2-4ac
Δ = -22-4·(-1)·143
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-24}{2*-1}=\frac{-22}{-2}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+24}{2*-1}=\frac{26}{-2}
=-13
$