1/7x-33/14=5/2x

Solution for 1/7x-33/14=5/2x equation:

1/7x-33/14=5/2x

We move all terms to the left:

1/7x-33/14-(5/2x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/7x-(+5/2x)-33/14=0

We get rid of parentheses

1/7x-5/2x-33/14=0

We calculate fractions


(-924x^2)/196x^2+28x/196x^2+(-490x)/196x^2=0

We multiply all the terms by the denominator


(-924x^2)+28x+(-490x)=0

We get rid of parentheses

-924x^2+28x-490x=0

We add all the numbers together, and all the variables

-924x^2-462x=0

a = -924; b = -462; c = 0;
Δ = b2-4ac
Δ = -4622-4·(-924)·0
Δ = 213444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{213444}=462$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-462)-462}{2*-924}=\frac{0}{-1848}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-462)+462}{2*-924}=\frac{924}{-1848}
=-1/2
$