3/2y-y-8=24

Solution for 3/2y-y-8=24 equation:

3/2y-y-8=24

We move all terms to the left:

3/2y-y-8-(24)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+3/2y-32=0

We multiply all the terms by the denominator


-1y*2y-32*2y+3=0

Wy multiply elements

-2y^2-64y+3=0

a = -2; b = -64; c = +3;
Δ = b2-4ac
Δ = -642-4·(-2)·3
Δ = 4120
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:

$\sqrt{\Delta}=\sqrt{4120}=\sqrt{4*1030}=\sqrt{4}*\sqrt{1030}=2\sqrt{1030}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-2\sqrt{1030}}{2*-2}=\frac{64-2\sqrt{1030}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+2\sqrt{1030}}{2*-2}=\frac{64+2\sqrt{1030}}{-4}
$