2/3y-1224;y=48

Solution for 2/3y-1224;y=48 equation:

2/3y-1224y=48

We move all terms to the left:

2/3y-1224y-(48)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

-1224y+2/3y-48=0

We multiply all the terms by the denominator


-1224y*3y-48*3y+2=0

Wy multiply elements

-3672y^2-144y+2=0

a = -3672; b = -144; c = +2;
Δ = b2-4ac
Δ = -1442-4·(-3672)·2
Δ = 50112
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:

$\sqrt{\Delta}=\sqrt{50112}=\sqrt{576*87}=\sqrt{576}*\sqrt{87}=24\sqrt{87}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-24\sqrt{87}}{2*-3672}=\frac{144-24\sqrt{87}}{-7344}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+24\sqrt{87}}{2*-3672}=\frac{144+24\sqrt{87}}{-7344}
$