-2x^2+x+2=-x-10

Solution for -2x^2+x+2=-x-10 equation:

-2x^2+x+2=-x-10

We move all terms to the left:

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

We add all the numbers together, and all the variables

-2x^2+x-(-1x-10)+2=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+2x+12=0

a = -2; b = 2; c = +12;
Δ = b2-4ac
Δ = 22-4·(-2)·12
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*-2}=\frac{8}{-4}
=-2
$