6/8y=15-y

Solution for 6/8y=15-y equation:

6/8y=15-y

We move all terms to the left:

6/8y-(15-y)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We add all the numbers together, and all the variables

6/8y-(-1y+15)=0

We get rid of parentheses

6/8y+1y-15=0

We multiply all the terms by the denominator


1y*8y-15*8y+6=0

Wy multiply elements

8y^2-120y+6=0

a = 8; b = -120; c = +6;
Δ = b2-4ac
Δ = -1202-4·8·6
Δ = 14208
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:

$\sqrt{\Delta}=\sqrt{14208}=\sqrt{64*222}=\sqrt{64}*\sqrt{222}=8\sqrt{222}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-8\sqrt{222}}{2*8}=\frac{120-8\sqrt{222}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+8\sqrt{222}}{2*8}=\frac{120+8\sqrt{222}}{16}
$