y-7=1/4y+8

Solution for y-7=1/4y+8 equation:

y-7=1/4y+8

We move all terms to the left:

y-7-(1/4y+8)=0


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

y∈R


We get rid of parentheses

y-1/4y-8-7=0

We multiply all the terms by the denominator


y*4y-8*4y-7*4y-1=0

Wy multiply elements

4y^2-32y-28y-1=0

We add all the numbers together, and all the variables

4y^2-60y-1=0

a = 4; b = -60; c = -1;
Δ = b2-4ac
Δ = -602-4·4·(-1)
Δ = 3616
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:

$\sqrt{\Delta}=\sqrt{3616}=\sqrt{16*226}=\sqrt{16}*\sqrt{226}=4\sqrt{226}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{226}}{2*4}=\frac{60-4\sqrt{226}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{226}}{2*4}=\frac{60+4\sqrt{226}}{8}
$