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

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

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

We move all terms to the left:

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


Domain of the equation: 7d!=0

d!=0/7

d!=0

d∈R



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

d∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

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