(3x+4)(2x-9)=0

Solution for (3x+4)(2x-9)=0 equation:

(3x+4)(2x-9)=0

We multiply parentheses ..

(+6x^2-27x+8x-36)=0

We get rid of parentheses

6x^2-27x+8x-36=0

We add all the numbers together, and all the variables

6x^2-19x-36=0

a = 6; b = -19; c = -36;
Δ = b2-4ac
Δ = -192-4·6·(-36)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-35}{2*6}=\frac{-16}{12}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+35}{2*6}=\frac{54}{12}
=4+1/2
$