8/x=5+1/2x

Solution for 8/x=5+1/2x equation:

8/x=5+1/2x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

8/x-1/2x-5=0

We calculate fractions


16x/2x^2+(-x)/2x^2-5=0

We add all the numbers together, and all the variables

16x/2x^2+(-1x)/2x^2-5=0

We multiply all the terms by the denominator


16x+(-1x)-5*2x^2=0

Wy multiply elements

-10x^2+16x+(-1x)=0

We get rid of parentheses

-10x^2+16x-1x=0

We add all the numbers together, and all the variables

-10x^2+15x=0

a = -10; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-10)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-10}=\frac{-30}{-20}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-10}=\frac{0}{-20}
=0
$