5/x=8-2x

Solution for 5/x=8-2x equation:

5/x=8-2x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

5/x+2x-8=0

We multiply all the terms by the denominator


2x*x-8*x+5=0

We add all the numbers together, and all the variables

-8x+2x*x+5=0

Wy multiply elements

2x^2-8x+5=0

a = 2; b = -8; c = +5;
Δ = b2-4ac
Δ = -82-4·2·5
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{6}}{2*2}=\frac{8-2\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{6}}{2*2}=\frac{8+2\sqrt{6}}{4}
$