-3(8-y)=61/2y-4

Solution for -3(8-y)=61/2y-4 equation:

-3(8-y)=61/2y-4

We move all terms to the left:

-3(8-y)-(61/2y-4)=0


Domain of the equation: 2y-4)!=0

y∈R


We add all the numbers together, and all the variables

-3(-1y+8)-(61/2y-4)=0

We multiply parentheses

3y-(61/2y-4)-24=0

We get rid of parentheses

3y-61/2y+4-24=0

We multiply all the terms by the denominator


3y*2y+4*2y-24*2y-61=0

Wy multiply elements

6y^2+8y-48y-61=0

We add all the numbers together, and all the variables

6y^2-40y-61=0

a = 6; b = -40; c = -61;
Δ = b2-4ac
Δ = -402-4·6·(-61)
Δ = 3064
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:

$\sqrt{\Delta}=\sqrt{3064}=\sqrt{4*766}=\sqrt{4}*\sqrt{766}=2\sqrt{766}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{766}}{2*6}=\frac{40-2\sqrt{766}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{766}}{2*6}=\frac{40+2\sqrt{766}}{12}
$