-x^2+12x=2x+9

Solution for -x^2+12x=2x+9 equation:

-x^2+12x=2x+9

We move all terms to the left:

-x^2+12x-(2x+9)=0

We add all the numbers together, and all the variables

-1x^2+12x-(2x+9)=0

We get rid of parentheses

-1x^2+12x-2x-9=0

We add all the numbers together, and all the variables

-1x^2+10x-9=0

a = -1; b = 10; c = -9;
Δ = b2-4ac
Δ = 102-4·(-1)·(-9)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-8}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+8}{2*-1}=\frac{-2}{-2}
=1
$