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

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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 $

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