(1/4)y-1=3y+2-8y

Solution for (1/4)y-1=3y+2-8y equation:

(1/4)y-1=3y+2-8y

We move all terms to the left:

(1/4)y-1-(3y+2-8y)=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-(-5y+2)-1=0

We multiply parentheses

y^2-(-5y+2)-1=0

We get rid of parentheses

y^2+5y-2-1=0

We add all the numbers together, and all the variables

y^2+5y-3=0

a = 1; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·1·(-3)
Δ = 37
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{-(5)-\sqrt{37}}{2*1}=\frac{-5-\sqrt{37}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{37}}{2*1}=\frac{-5+\sqrt{37}}{2}
$