(1/4)y-3=5-2y

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

(1/4)y-3=5-2y

We move all terms to the left:

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


Domain of the equation: 4)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

y^2-(-2y+5)-3=0

We get rid of parentheses

y^2+2y-5-3=0

We add all the numbers together, and all the variables

y^2+2y-8=0

a = 1; b = 2; c = -8;
Δ = b2-4ac
Δ = 22-4·1·(-8)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*1}=\frac{-8}{2}
=-4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*1}=\frac{4}{2}
=2
$