y-3/4y=11

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

y-3/4y=11

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We multiply all the terms by the denominator


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

Wy multiply elements

4y^2-44y-3=0

a = 4; b = -44; c = -3;
Δ = b2-4ac
Δ = -442-4·4·(-3)
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*4}=\frac{44-8\sqrt{31}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+8\sqrt{31}}{2*4}=\frac{44+8\sqrt{31}}{8}
$