(x-5)(10-4x)=0

Solution for (x-5)(10-4x)=0 equation:

(x-5)(10-4x)=0

We add all the numbers together, and all the variables

(x-5)(-4x+10)=0

We multiply parentheses ..

(-4x^2+10x+20x-50)=0

We get rid of parentheses

-4x^2+10x+20x-50=0

We add all the numbers together, and all the variables

-4x^2+30x-50=0

a = -4; b = 30; c = -50;
Δ = b2-4ac
Δ = 302-4·(-4)·(-50)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10}{2*-4}=\frac{-40}{-8}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10}{2*-4}=\frac{-20}{-8}
=2+1/2
$