y-6/7y=9

Solution for y-6/7y=9 equation:

y-6/7y=9

We move all terms to the left:

y-6/7y-(9)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We multiply all the terms by the denominator


y*7y-9*7y-6=0

Wy multiply elements

7y^2-63y-6=0

a = 7; b = -63; c = -6;
Δ = b2-4ac
Δ = -632-4·7·(-6)
Δ = 4137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-\sqrt{4137}}{2*7}=\frac{63-\sqrt{4137}}{14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{4137}}{2*7}=\frac{63+\sqrt{4137}}{14}
$