-x^2-9x=2x-6

Solution for -x^2-9x=2x-6 equation:

-x^2-9x=2x-6

We move all terms to the left:

-x^2-9x-(2x-6)=0

We add all the numbers together, and all the variables

-1x^2-9x-(2x-6)=0

We get rid of parentheses

-1x^2-9x-2x+6=0

We add all the numbers together, and all the variables

-1x^2-11x+6=0

a = -1; b = -11; c = +6;
Δ = b2-4ac
Δ = -112-4·(-1)·6
Δ = 145
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{-(-11)-\sqrt{145}}{2*-1}=\frac{11-\sqrt{145}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{145}}{2*-1}=\frac{11+\sqrt{145}}{-2}
$