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

Solution for (-2x+9)(12+x)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-2x^2-24x+9x+108)=0

We get rid of parentheses

-2x^2-24x+9x+108=0

We add all the numbers together, and all the variables

-2x^2-15x+108=0

a = -2; b = -15; c = +108;
Δ = b2-4ac
Δ = -152-4·(-2)·108
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-33}{2*-2}=\frac{-18}{-4}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+33}{2*-2}=\frac{48}{-4}
=-12
$