1/4y=3y-11

Solution for 1/4y=3y-11 equation:

1/4y=3y-11

We move all terms to the left:

1/4y-(3y-11)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We get rid of parentheses

1/4y-3y+11=0

We multiply all the terms by the denominator


-3y*4y+11*4y+1=0

Wy multiply elements

-12y^2+44y+1=0

a = -12; b = 44; c = +1;
Δ = b2-4ac
Δ = 442-4·(-12)·1
Δ = 1984
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:

$\sqrt{\Delta}=\sqrt{1984}=\sqrt{64*31}=\sqrt{64}*\sqrt{31}=8\sqrt{31}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-8\sqrt{31}}{2*-12}=\frac{-44-8\sqrt{31}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+8\sqrt{31}}{2*-12}=\frac{-44+8\sqrt{31}}{-24}
$