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10/2x-2(x-10)=11
We move all terms to the left:
10/2x-2(x-10)-(11)=0
Domain of the equation: 2x!=0We multiply parentheses
x!=0/2
x!=0
x∈R
10/2x-2x+20-11=0
We multiply all the terms by the denominator
-2x*2x+20*2x-11*2x+10=0
Wy multiply elements
-4x^2+40x-22x+10=0
We add all the numbers together, and all the variables
-4x^2+18x+10=0
a = -4; b = 18; c = +10;
Δ = b2-4ac
Δ = 182-4·(-4)·10
Δ = 484
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{484}=22$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-22}{2*-4}=\frac{-40}{-8} =+5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+22}{2*-4}=\frac{4}{-8} =-1/2 $
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