4y+3/4y-8=y

Solution for 4y+3/4y-8=y equation:

4y+3/4y-8=y

We move all terms to the left:

4y+3/4y-8-(y)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

3y+3/4y-8=0

We multiply all the terms by the denominator


3y*4y-8*4y+3=0

Wy multiply elements

12y^2-32y+3=0

a = 12; b = -32; c = +3;
Δ = b2-4ac
Δ = -322-4·12·3
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{55}}{2*12}=\frac{32-4\sqrt{55}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{55}}{2*12}=\frac{32+4\sqrt{55}}{24}
$