1/5x=14.2-2x

Solution for 1/5x=14.2-2x equation:

1/5x=14.2-2x

We move all terms to the left:

1/5x-(14.2-2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(-2x+14.2)=0

We get rid of parentheses

1/5x+2x-14.2=0

We multiply all the terms by the denominator


2x*5x-(14.2)*5x+1=0

We multiply parentheses

2x*5x-71x+1=0

Wy multiply elements

10x^2-71x+1=0

a = 10; b = -71; c = +1;
Δ = b2-4ac
Δ = -712-4·10·1
Δ = 5001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-71)-\sqrt{5001}}{2*10}=\frac{71-\sqrt{5001}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+\sqrt{5001}}{2*10}=\frac{71+\sqrt{5001}}{20}
$