24=9/2y-39y

Solution for 24=9/2y-39y equation:

24=9/2y-39y

We move all terms to the left:

24-(9/2y-39y)=0


Domain of the equation: 2y-39y)!=0

y∈R


We add all the numbers together, and all the variables

-(-39y+9/2y)+24=0

We get rid of parentheses

39y-9/2y+24=0

We multiply all the terms by the denominator


39y*2y+24*2y-9=0

Wy multiply elements

78y^2+48y-9=0

a = 78; b = 48; c = -9;
Δ = b2-4ac
Δ = 482-4·78·(-9)
Δ = 5112
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:

$\sqrt{\Delta}=\sqrt{5112}=\sqrt{36*142}=\sqrt{36}*\sqrt{142}=6\sqrt{142}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{142}}{2*78}=\frac{-48-6\sqrt{142}}{156}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{142}}{2*78}=\frac{-48+6\sqrt{142}}{156}
$