(5x+6)(3-4x)=0

Solution for (5x+6)(3-4x)=0 equation:

(5x+6)(3-4x)=0

We add all the numbers together, and all the variables

(5x+6)(-4x+3)=0

We multiply parentheses ..

(-20x^2+15x-24x+18)=0

We get rid of parentheses

-20x^2+15x-24x+18=0

We add all the numbers together, and all the variables

-20x^2-9x+18=0

a = -20; b = -9; c = +18;
Δ = b2-4ac
Δ = -92-4·(-20)·18
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-39}{2*-20}=\frac{-30}{-40}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+39}{2*-20}=\frac{48}{-40}
=-1+1/5
$