6y-7/3y=9=1/3

Solution for 6y-7/3y=9=1/3 equation:

6y-7/3y=9=1/3

We move all terms to the left:

6y-7/3y-(9)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We multiply all the terms by the denominator


6y*3y-9*3y-7=0

Wy multiply elements

18y^2-27y-7=0

a = 18; b = -27; c = -7;
Δ = b2-4ac
Δ = -272-4·18·(-7)
Δ = 1233
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:

$\sqrt{\Delta}=\sqrt{1233}=\sqrt{9*137}=\sqrt{9}*\sqrt{137}=3\sqrt{137}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{137}}{2*18}=\frac{27-3\sqrt{137}}{36}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{137}}{2*18}=\frac{27+3\sqrt{137}}{36}
$