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

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

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

We move all terms to the left:

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


Domain of the equation: 7a!=0

a!=0/7

a!=0

a∈R



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

a∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2646a^2+63a=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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-63}{2*-2646}=\frac{-126}{-5292}
=1/42
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*-2646}=\frac{0}{-5292}
=0
$