(2x-8)(x-1)/(4-x)=0

Solution for (2x-8)(x-1)/(4-x)=0 equation:

(2x-8)(x-1)/(4-x)=0


Domain of the equation: (4-x)!=0

We move all terms containing x to the left, all other terms to the right

-x!=-4

x!=-4/-1

x!=+4

x∈R


We add all the numbers together, and all the variables

(2x-8)(x-1)/(-1x+4)=0

We multiply parentheses ..

(+2x^2-2x-8x+8)/(-1x+4)=0

We multiply all the terms by the denominator


(+2x^2-2x-8x+8)=0

We get rid of parentheses

2x^2-2x-8x+8=0

We add all the numbers together, and all the variables

2x^2-10x+8=0

a = 2; b = -10; c = +8;
Δ = b2-4ac
Δ = -102-4·2·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6}{2*2}=\frac{16}{4}
=4
$