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

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

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

We move all terms to the left:

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


Domain of the equation: 7h!=0

h!=0/7

h!=0

h∈R



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

h∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

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