5/2x-1/14=2/3x

Solution for 5/2x-1/14=2/3x equation:

5/2x-1/14=2/3x

We move all terms to the left:

5/2x-1/14-(2/3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x-(+2/3x)-1/14=0

We get rid of parentheses

5/2x-2/3x-1/14=0

We calculate fractions


(-18x^2)/84x^2+210x/84x^2+(-56x)/84x^2=0

We multiply all the terms by the denominator


(-18x^2)+210x+(-56x)=0

We get rid of parentheses

-18x^2+210x-56x=0

We add all the numbers together, and all the variables

-18x^2+154x=0

a = -18; b = 154; c = 0;
Δ = b2-4ac
Δ = 1542-4·(-18)·0
Δ = 23716
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{23716}=154$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(154)-154}{2*-18}=\frac{-308}{-36}
=8+5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(154)+154}{2*-18}=\frac{0}{-36}
=0
$