1/4y-3=6-2y

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

1/4y-3=6-2y

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/4y+2y-6-3=0

We multiply all the terms by the denominator


2y*4y-6*4y-3*4y+1=0

Wy multiply elements

8y^2-24y-12y+1=0

We add all the numbers together, and all the variables

8y^2-36y+1=0

a = 8; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·8·1
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{79}}{2*8}=\frac{36-4\sqrt{79}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{79}}{2*8}=\frac{36+4\sqrt{79}}{16}
$