3/7y-9=14y

Solution for 3/7y-9=14y equation:

3/7y-9=14y

We move all terms to the left:

3/7y-9-(14y)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We add all the numbers together, and all the variables

-14y+3/7y-9=0

We multiply all the terms by the denominator


-14y*7y-9*7y+3=0

Wy multiply elements

-98y^2-63y+3=0

a = -98; b = -63; c = +3;
Δ = b2-4ac
Δ = -632-4·(-98)·3
Δ = 5145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5145}=\sqrt{49*105}=\sqrt{49}*\sqrt{105}=7\sqrt{105}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-7\sqrt{105}}{2*-98}=\frac{63-7\sqrt{105}}{-196}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+7\sqrt{105}}{2*-98}=\frac{63+7\sqrt{105}}{-196}
$