5(2x+3)-(2x+3)(3x-4)=0

Solution for 5(2x+3)-(2x+3)(3x-4)=0 equation:

5(2x+3)-(2x+3)(3x-4)=0

We multiply parentheses

10x-(2x+3)(3x-4)+15=0

We multiply parentheses ..

-(+6x^2-8x+9x-12)+10x+15=0

We get rid of parentheses

-6x^2+8x-9x+10x+12+15=0

We add all the numbers together, and all the variables

-6x^2+9x+27=0

a = -6; b = 9; c = +27;
Δ = b2-4ac
Δ = 92-4·(-6)·27
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-27}{2*-6}=\frac{-36}{-12}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+27}{2*-6}=\frac{18}{-12}
=-1+1/2
$