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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-10x^2+23x-12=0

a = -10; b = 23; c = -12;
Δ = b2-4ac
Δ = 232-4·(-10)·(-12)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-7}{2*-10}=\frac{-30}{-20}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+7}{2*-10}=\frac{-16}{-20}
=4/5
$