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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -24; b = 2; c = +15;
Δ = b2-4ac
Δ = 22-4·(-24)·15
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-38}{2*-24}=\frac{-40}{-48}
=5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+38}{2*-24}=\frac{36}{-48}
=-3/4
$