4/2x=30-0.2x

Solution for 4/2x=30-0.2x equation:

4/2x=30-0.2x

We move all terms to the left:

4/2x-(30-0.2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4/2x-(-0.2x+30)=0

We get rid of parentheses

4/2x+0.2x-30=0

We multiply all the terms by the denominator


(0.2x)*2x-30*2x+4=0

We add all the numbers together, and all the variables

(+0.2x)*2x-30*2x+4=0

We multiply parentheses

0x^2-30*2x+4=0

Wy multiply elements

0x^2-60x+4=0

We add all the numbers together, and all the variables

x^2-60x+4=0

a = 1; b = -60; c = +4;
Δ = b2-4ac
Δ = -602-4·1·4
Δ = 3584
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:

$\sqrt{\Delta}=\sqrt{3584}=\sqrt{256*14}=\sqrt{256}*\sqrt{14}=16\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-16\sqrt{14}}{2*1}=\frac{60-16\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+16\sqrt{14}}{2*1}=\frac{60+16\sqrt{14}}{2}
$