4x/x+1=x/2

Solution for 4x/x+1=x/2 equation:

4x/x+1=x/2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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
$