(2x-1)(4-3x)=0

Solution for (2x-1)(4-3x)=0 equation:

(2x-1)(4-3x)=0

We add all the numbers together, and all the variables

(2x-1)(-3x+4)=0

We multiply parentheses ..

(-6x^2+8x+3x-4)=0

We get rid of parentheses

-6x^2+8x+3x-4=0

We add all the numbers together, and all the variables

-6x^2+11x-4=0

a = -6; b = 11; c = -4;
Δ = b2-4ac
Δ = 112-4·(-6)·(-4)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-5}{2*-6}=\frac{-16}{-12}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5}{2*-6}=\frac{-6}{-12}
=1/2
$