-2x(x+5)=12+9x

Solution for -2x(x+5)=12+9x equation:

-2x(x+5)=12+9x

We move all terms to the left:

-2x(x+5)-(12+9x)=0

We add all the numbers together, and all the variables

-2x(x+5)-(9x+12)=0

We multiply parentheses

-2x^2-10x-(9x+12)=0

We get rid of parentheses

-2x^2-10x-9x-12=0

We add all the numbers together, and all the variables

-2x^2-19x-12=0

a = -2; b = -19; c = -12;
Δ = b2-4ac
Δ = -192-4·(-2)·(-12)
Δ = 265
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{-(-19)-\sqrt{265}}{2*-2}=\frac{19-\sqrt{265}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{265}}{2*-2}=\frac{19+\sqrt{265}}{-4}
$