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2x-4/(x-1)=10
We move all terms to the left:
2x-4/(x-1)-(10)=0
Domain of the equation: (x-1)!=0We multiply all the terms by the denominator
We move all terms containing x to the left, all other terms to the right
x!=1
x∈R
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} $
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