22/4y+24=3y

Solution for 22/4y+24=3y equation:

22/4y+24=3y

We move all terms to the left:

22/4y+24-(3y)=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+22/4y+24=0

We multiply all the terms by the denominator


-3y*4y+24*4y+22=0

Wy multiply elements

-12y^2+96y+22=0

a = -12; b = 96; c = +22;
Δ = b2-4ac
Δ = 962-4·(-12)·22
Δ = 10272
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:

$\sqrt{\Delta}=\sqrt{10272}=\sqrt{16*642}=\sqrt{16}*\sqrt{642}=4\sqrt{642}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-4\sqrt{642}}{2*-12}=\frac{-96-4\sqrt{642}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+4\sqrt{642}}{2*-12}=\frac{-96+4\sqrt{642}}{-24}
$