3/7x-5=8-3/14x

Solution for 3/7x-5=8-3/14x equation:

3/7x-5=8-3/14x

We move all terms to the left:

3/7x-5-(8-3/14x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 14x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/7x-(-3/14x+8)-5=0

We get rid of parentheses

3/7x+3/14x-8-5=0

We calculate fractions


42x/98x^2+21x/98x^2-8-5=0

We add all the numbers together, and all the variables

42x/98x^2+21x/98x^2-13=0

We multiply all the terms by the denominator


42x+21x-13*98x^2=0

We add all the numbers together, and all the variables

63x-13*98x^2=0

Wy multiply elements

-1274x^2+63x=0

a = -1274; b = 63; c = 0;
Δ = b2-4ac
Δ = 632-4·(-1274)·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-63}{2*-1274}=\frac{-126}{-2548}
=9/182
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*-1274}=\frac{0}{-2548}
=0
$