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4x/x+1=x/2
We move all terms to the left:
4x/x+1-(x/2)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
4x/x-(+x/2)+1=0
We get rid of parentheses
4x/x-x/2+1=0
We calculate fractions
(-1x^2)/2x+8x/2x+1=0
We multiply all the terms by the denominator
(-1x^2)+8x+1*2x=0
Wy multiply elements
(-1x^2)+8x+2x=0
We get rid of parentheses
-1x^2+8x+2x=0
We add all the numbers together, and all the variables
-1x^2+10x=0
a = -1; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-1)·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-1}=\frac{-20}{-2} =+10 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-1}=\frac{0}{-2} =0 $
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