y=4y+3/4y-8

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

y=4y+3/4y-8

We move all terms to the left:

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


Domain of the equation: 4y-8)!=0

y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4y^2-16y^2+32y-3=0

We add all the numbers together, and all the variables

-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}
$