3,75y+18+5.4/3y=6,5+30

Solution for 3,75y+18+5.4/3y=6,5+30 equation:

3.75y+18+5.4/3y=6.5+30

We move all terms to the left:

3.75y+18+5.4/3y-(6.5+30)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

3.75y+5.4/3y+18-(36.5)=0

We add all the numbers together, and all the variables

3.75y+5.4/3y-18.5=0

We multiply all the terms by the denominator


(3.75y)*3y-(18.5)*3y+5.4=0

We add all the numbers together, and all the variables

(+3.75y)*3y-(18.5)*3y+5.4=0

We multiply parentheses

9y^2-55.5y+5.4=0

a = 9; b = -55.5; c = +5.4;
Δ = b2-4ac
Δ = -55.52-4·9·5.4
Δ = 2885.85
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{-(-55.5)-\sqrt{2885.85}}{2*9}=\frac{55.5-\sqrt{2885.85}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55.5)+\sqrt{2885.85}}{2*9}=\frac{55.5+\sqrt{2885.85}}{18}
$