4/x=x/2x+5

Solution for 4/x=x/2x+5 equation:

4/x=x/2x+5

We move all terms to the left:

4/x-(x/2x+5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

4/x-x/2x-5=0

We calculate fractions


(-1x^2)/2x^2+8x/2x^2-5=0

We multiply all the terms by the denominator


(-1x^2)+8x-5*2x^2=0

Wy multiply elements

(-1x^2)-10x^2+8x=0

We get rid of parentheses

-1x^2-10x^2+8x=0

We add all the numbers together, and all the variables

-11x^2+8x=0

a = -11; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-11)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-11}=\frac{-16}{-22}
=8/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-11}=\frac{0}{-22}
=0
$