2x-4/(x-1)=10

Solution for 2x-4/(x-1)=10 equation:

2x-4/(x-1)=10

We move all terms to the left:

2x-4/(x-1)-(10)=0


Domain of the equation: (x-1)!=0

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

x!=1

x∈R


We multiply all the terms by the denominator


2x*(x-1)-10*(x-1)-4=0

We multiply parentheses

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

We add all the numbers together, and all the variables

2x^2-12x+6=0

a = 2; b = -12; c = +6;
Δ = b2-4ac
Δ = -122-4·2·6
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{6}}{2*2}=\frac{12-4\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{6}}{2*2}=\frac{12+4\sqrt{6}}{4}
$