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

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

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

We add all the numbers together, and all the variables

(-1x+4)(5x-3)=0

We multiply parentheses ..

(-5x^2+3x+20x-12)=0

We get rid of parentheses

-5x^2+3x+20x-12=0

We add all the numbers together, and all the variables

-5x^2+23x-12=0

a = -5; b = 23; c = -12;
Δ = b2-4ac
Δ = 232-4·(-5)·(-12)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-17}{2*-5}=\frac{-40}{-10}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+17}{2*-5}=\frac{-6}{-10}
=3/5
$