1/8y+2=-y+11

Solution for 1/8y+2=-y+11 equation:

1/8y+2=-y+11

We move all terms to the left:

1/8y+2-(-y+11)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We add all the numbers together, and all the variables

1/8y-(-1y+11)+2=0

We get rid of parentheses

1/8y+1y-11+2=0

We multiply all the terms by the denominator


1y*8y-11*8y+2*8y+1=0

Wy multiply elements

8y^2-88y+16y+1=0

We add all the numbers together, and all the variables

8y^2-72y+1=0

a = 8; b = -72; c = +1;
Δ = b2-4ac
Δ = -722-4·8·1
Δ = 5152
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:

$\sqrt{\Delta}=\sqrt{5152}=\sqrt{16*322}=\sqrt{16}*\sqrt{322}=4\sqrt{322}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{322}}{2*8}=\frac{72-4\sqrt{322}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{322}}{2*8}=\frac{72+4\sqrt{322}}{16}
$