3y-7/4y-9=6

Solution for 3y-7/4y-9=6 equation:

3y-7/4y-9=6

We move all terms to the left:

3y-7/4y-9-(6)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

3y-7/4y-15=0

We multiply all the terms by the denominator


3y*4y-15*4y-7=0

Wy multiply elements

12y^2-60y-7=0

a = 12; b = -60; c = -7;
Δ = b2-4ac
Δ = -602-4·12·(-7)
Δ = 3936
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:

$\sqrt{\Delta}=\sqrt{3936}=\sqrt{16*246}=\sqrt{16}*\sqrt{246}=4\sqrt{246}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{246}}{2*12}=\frac{60-4\sqrt{246}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{246}}{2*12}=\frac{60+4\sqrt{246}}{24}
$