3(8-y)=6(1/2y-4)

Solution for 3(8-y)=6(1/2y-4) equation:

3(8-y)=6(1/2y-4)

We move all terms to the left:

3(8-y)-(6(1/2y-4))=0


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

y∈R


We add all the numbers together, and all the variables

3(-1y+8)-(6(1/2y-4))=0

We multiply parentheses

-3y-(6(1/2y-4))+24=0

We multiply all the terms by the denominator


-3y*2y+24*2y-4))-(6(1-4))=0

We add all the numbers together, and all the variables

-3y*2y+24*2y-4))-(6(-3))=0

We add all the numbers together, and all the variables

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

Wy multiply elements

-6y^2+48y=0

a = -6; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·(-6)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*-6}=\frac{-96}{-12}
=+8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*-6}=\frac{0}{-12}
=0
$