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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-3x^2+4x+15x-20)=0

We get rid of parentheses

-3x^2+4x+15x-20=0

We add all the numbers together, and all the variables

-3x^2+19x-20=0

a = -3; b = 19; c = -20;
Δ = b2-4ac
Δ = 192-4·(-3)·(-20)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-11}{2*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+11}{2*-3}=\frac{-8}{-6}
=1+1/3
$