3,75y+18+5.3/4y=6,5y+30

Solution for 3,75y+18+5.3/4y=6,5y+30 equation:

3.75y+18+5.3/4y=6.5y+30

We move all terms to the left:

3.75y+18+5.3/4y-(6.5y+30)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We get rid of parentheses

3.75y+5.3/4y-6.5y-30+18=0

We multiply all the terms by the denominator


(3.75y)*4y-(6.5y)*4y-30*4y+18*4y+5.3=0

We add all the numbers together, and all the variables

(+3.75y)*4y-(+6.5y)*4y-30*4y+18*4y+5.3=0

We multiply parentheses

12y^2-24y^2-30*4y+18*4y+5.3=0

Wy multiply elements

12y^2-24y^2-120y+72y+5.3=0

We add all the numbers together, and all the variables

-12y^2-48y+5.3=0

a = -12; b = -48; c = +5.3;
Δ = b2-4ac
Δ = -482-4·(-12)·5.3
Δ = 2558.4
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{-(-48)-\sqrt{2558.4}}{2*-12}=\frac{48-\sqrt{2558.4}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+\sqrt{2558.4}}{2*-12}=\frac{48+\sqrt{2558.4}}{-24}
$