(2x+3)(x-9)=0

Solution for (2x+3)(x-9)=0 equation:

(2x+3)(x-9)=0

We multiply parentheses ..

(+2x^2-18x+3x-27)=0

We get rid of parentheses

2x^2-18x+3x-27=0

We add all the numbers together, and all the variables

2x^2-15x-27=0

a = 2; b = -15; c = -27;
Δ = b2-4ac
Δ = -152-4·2·(-27)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-21}{2*2}=\frac{-6}{4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+21}{2*2}=\frac{36}{4}
=9
$