5/7x=14-2x

Solution for 5/7x=14-2x equation:

5/7x=14-2x

We move all terms to the left:

5/7x-(14-2x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

5/7x-(-2x+14)=0

We get rid of parentheses

5/7x+2x-14=0

We multiply all the terms by the denominator


2x*7x-14*7x+5=0

Wy multiply elements

14x^2-98x+5=0

a = 14; b = -98; c = +5;
Δ = b2-4ac
Δ = -982-4·14·5
Δ = 9324
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:

$\sqrt{\Delta}=\sqrt{9324}=\sqrt{36*259}=\sqrt{36}*\sqrt{259}=6\sqrt{259}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-6\sqrt{259}}{2*14}=\frac{98-6\sqrt{259}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+6\sqrt{259}}{2*14}=\frac{98+6\sqrt{259}}{28}
$