5/7x-7/2x-3=3/14

Solution for 5/7x-7/2x-3=3/14 equation:

5/7x-7/2x-3=3/14

We move all terms to the left:

5/7x-7/2x-3-(3/14)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5/7x-7/2x-3-(+3/14)=0

We get rid of parentheses

5/7x-7/2x-3-3/14=0

We calculate fractions


(-84x^2)/196x^2+140x/196x^2+(-686x)/196x^2-3=0

We multiply all the terms by the denominator


(-84x^2)+140x+(-686x)-3*196x^2=0

Wy multiply elements

(-84x^2)-588x^2+140x+(-686x)=0

We get rid of parentheses

-84x^2-588x^2+140x-686x=0

We add all the numbers together, and all the variables

-672x^2-546x=0

a = -672; b = -546; c = 0;
Δ = b2-4ac
Δ = -5462-4·(-672)·0
Δ = 298116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{298116}=546$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-546)-546}{2*-672}=\frac{0}{-1344}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-546)+546}{2*-672}=\frac{1092}{-1344}
=-13/16
$