6+0.5y=-2(3-1/4y)

Solution for 6+0.5y=-2(3-1/4y) equation:

6+0.5y=-2(3-1/4y)

We move all terms to the left:

6+0.5y-(-2(3-1/4y))=0


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

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

0.5y-(-2(-1/4y+3))+6=0

We multiply all the terms by the denominator


(0.5y)*4y+6*4y-1+3))-(-2(+3))=0

We add all the numbers together, and all the variables

(+0.5y)*4y+6*4y-1+3))-(-23)=0

We add all the numbers together, and all the variables

(+0.5y)*4y+6*4y=0

We multiply parentheses

0y^2+6*4y=0

Wy multiply elements

0y^2+24y=0

We add all the numbers together, and all the variables

y^2+24y=0

a = 1; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·1·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*1}=\frac{-48}{2}
=-24
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*1}=\frac{0}{2}
=0
$