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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-18x^2+39x-20=0

a = -18; b = 39; c = -20;
Δ = b2-4ac
Δ = 392-4·(-18)·(-20)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-9}{2*-18}=\frac{-48}{-36}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+9}{2*-18}=\frac{-30}{-36}
=5/6
$