(1.5/5y)+y=16.25

Solution for (1.5/5y)+y=16.25 equation:

(1.5/5y)+y=16.25

We move all terms to the left:

(1.5/5y)+y-(16.25)=0


Domain of the equation: 5y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+1.5/5y)+y-(16.25)=0

We add all the numbers together, and all the variables

y+(+1.5/5y)-16.25=0

We get rid of parentheses

y+1.5/5y-16.25=0

We multiply all the terms by the denominator


y*5y-(16.25)*5y+1.5=0

We multiply parentheses

y*5y-81.25y+1.5=0

Wy multiply elements

5y^2-81.25y+1.5=0

a = 5; b = -81.25; c = +1.5;
Δ = b2-4ac
Δ = -81.252-4·5·1.5
Δ = 6571.5625
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{-(-81.25)-\sqrt{6571.5625}}{2*5}=\frac{81.25-\sqrt{6571.5625}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81.25)+\sqrt{6571.5625}}{2*5}=\frac{81.25+\sqrt{6571.5625}}{10}
$