4/x=6/0.2-x

Solution for 4/x=6/0.2-x equation:

4/x=6/0.2-x

We move all terms to the left:

4/x-(6/0.2-x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 0.2-x)!=0

We move all terms containing x to the left, all other terms to the right

-x)!=-0.2

x!=-0.2/1

x!=-0.2

x∈R


We add all the numbers together, and all the variables

4/x-(-1x+30)=0

We get rid of parentheses

4/x+1x-30=0

We multiply all the terms by the denominator


1x*x-30*x+4=0

We add all the numbers together, and all the variables

-30x+1x*x+4=0

Wy multiply elements

x^2-30x+4=0

a = 1; b = -30; c = +4;
Δ = b2-4ac
Δ = -302-4·1·4
Δ = 884
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:

$\sqrt{\Delta}=\sqrt{884}=\sqrt{4*221}=\sqrt{4}*\sqrt{221}=2\sqrt{221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{221}}{2*1}=\frac{30-2\sqrt{221}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{221}}{2*1}=\frac{30+2\sqrt{221}}{2}
$