4/7x-15=6+1/14x

Solution for 4/7x-15=6+1/14x equation:

4/7x-15=6+1/14x

We move all terms to the left:

4/7x-15-(6+1/14x)=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

4/7x-(1/14x+6)-15=0

We get rid of parentheses

4/7x-1/14x-6-15=0

We calculate fractions


56x/98x^2+(-7x)/98x^2-6-15=0

We add all the numbers together, and all the variables

56x/98x^2+(-7x)/98x^2-21=0

We multiply all the terms by the denominator


56x+(-7x)-21*98x^2=0

Wy multiply elements

-2058x^2+56x+(-7x)=0

We get rid of parentheses

-2058x^2+56x-7x=0

We add all the numbers together, and all the variables

-2058x^2+49x=0

a = -2058; b = 49; c = 0;
Δ = b2-4ac
Δ = 492-4·(-2058)·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-49}{2*-2058}=\frac{-98}{-4116}
=1/42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+49}{2*-2058}=\frac{0}{-4116}
=0
$