4/x=18-2x

Solution for 4/x=18-2x equation:

4/x=18-2x

We move all terms to the left:

4/x-(18-2x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4/x-(-2x+18)=0

We get rid of parentheses

4/x+2x-18=0

We multiply all the terms by the denominator


2x*x-18*x+4=0

We add all the numbers together, and all the variables

-18x+2x*x+4=0

Wy multiply elements

2x^2-18x+4=0

a = 2; b = -18; c = +4;
Δ = b2-4ac
Δ = -182-4·2·4
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{73}}{2*2}=\frac{18-2\sqrt{73}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{73}}{2*2}=\frac{18+2\sqrt{73}}{4}
$