6/7x-12=3/14x+15

Solution for 6/7x-12=3/14x+15 equation:

6/7x-12=3/14x+15

We move all terms to the left:

6/7x-12-(3/14x+15)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 14x+15)!=0

x∈R


We get rid of parentheses

6/7x-3/14x-15-12=0

We calculate fractions


84x/98x^2+(-21x)/98x^2-15-12=0

We add all the numbers together, and all the variables

84x/98x^2+(-21x)/98x^2-27=0

We multiply all the terms by the denominator


84x+(-21x)-27*98x^2=0

Wy multiply elements

-2646x^2+84x+(-21x)=0

We get rid of parentheses

-2646x^2+84x-21x=0

We add all the numbers together, and all the variables

-2646x^2+63x=0

a = -2646; b = 63; c = 0;
Δ = b2-4ac
Δ = 632-4·(-2646)·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*-2646}=\frac{-126}{-5292}
=1/42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*-2646}=\frac{0}{-5292}
=0
$