3/8y-6y=-24

Solution for 3/8y-6y=-24 equation:

3/8y-6y=-24

We move all terms to the left:

3/8y-6y-(-24)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We add all the numbers together, and all the variables

-6y+3/8y+24=0

We multiply all the terms by the denominator


-6y*8y+24*8y+3=0

Wy multiply elements

-48y^2+192y+3=0

a = -48; b = 192; c = +3;
Δ = b2-4ac
Δ = 1922-4·(-48)·3
Δ = 37440
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:

$\sqrt{\Delta}=\sqrt{37440}=\sqrt{576*65}=\sqrt{576}*\sqrt{65}=24\sqrt{65}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-24\sqrt{65}}{2*-48}=\frac{-192-24\sqrt{65}}{-96}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+24\sqrt{65}}{2*-48}=\frac{-192+24\sqrt{65}}{-96}
$