1/8y-16.3=1.9y+13.3

Solution for 1/8y-16.3=1.9y+13.3 equation:

1/8y-16.3=1.9y+13.3

We move all terms to the left:

1/8y-16.3-(1.9y+13.3)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We get rid of parentheses

1/8y-1.9y-13.3-16.3=0

We multiply all the terms by the denominator


-(1.9y)*8y-(13.3)*8y-(16.3)*8y+1=0

We add all the numbers together, and all the variables

-(+1.9y)*8y-(13.3)*8y-(16.3)*8y+1=0

We multiply parentheses

-8y^2-106.4y-130.4y+1=0

We add all the numbers together, and all the variables

-8y^2-236.8y+1=0

a = -8; b = -236.8; c = +1;
Δ = b2-4ac
Δ = -236.82-4·(-8)·1
Δ = 56106.24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-236.8)-\sqrt{56106.24}}{2*-8}=\frac{236.8-\sqrt{56106.24}}{-16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-236.8)+\sqrt{56106.24}}{2*-8}=\frac{236.8+\sqrt{56106.24}}{-16}
$