.1/4y-3=5-2y

Solution for .1/4y-3=5-2y equation:

.1/4y-3=5-2y

We move all terms to the left:

.1/4y-3-(5-2y)=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+5)-3=0

We get rid of parentheses

.1/4y+2y-5-3=0

We multiply all the terms by the denominator


2y*4y-5*4y-3*4y+.1=0

We add all the numbers together, and all the variables

2y*4y-5*4y-3*4y+0.1=0

Wy multiply elements

8y^2-20y-12y+0.1=0

We add all the numbers together, and all the variables

8y^2-32y+0.1=0

a = 8; b = -32; c = +0.1;
Δ = b2-4ac
Δ = -322-4·8·0.1
Δ = 1020.8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-\sqrt{1020.8}}{2*8}=\frac{32-\sqrt{1020.8}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+\sqrt{1020.8}}{2*8}=\frac{32+\sqrt{1020.8}}{16}
$