(1)/(8)y+17=2y-118

Solution for (1)/(8)y+17=2y-118 equation:

(1)/(8)y+17=2y-118

We move all terms to the left:

(1)/(8)y+17-(2y-118)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We get rid of parentheses

1/8y-2y+118+17=0

We multiply all the terms by the denominator


-2y*8y+118*8y+17*8y+1=0

Wy multiply elements

-16y^2+944y+136y+1=0

We add all the numbers together, and all the variables

-16y^2+1080y+1=0

a = -16; b = 1080; c = +1;
Δ = b2-4ac
Δ = 10802-4·(-16)·1
Δ = 1166464
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:

$\sqrt{\Delta}=\sqrt{1166464}=\sqrt{64*18226}=\sqrt{64}*\sqrt{18226}=8\sqrt{18226}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1080)-8\sqrt{18226}}{2*-16}=\frac{-1080-8\sqrt{18226}}{-32}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1080)+8\sqrt{18226}}{2*-16}=\frac{-1080+8\sqrt{18226}}{-32}
$