5y-51.25=-3+3/4y

Solution for 5y-51.25=-3+3/4y equation:

5y-51.25=-3+3/4y

We move all terms to the left:

5y-51.25-(-3+3/4y)=0


Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

5y-(3/4y-3)-51.25=0

We get rid of parentheses

5y-3/4y+3-51.25=0

We multiply all the terms by the denominator


5y*4y+3*4y-(51.25)*4y-3=0

We multiply parentheses

5y*4y+3*4y-205y-3=0

Wy multiply elements

20y^2+12y-205y-3=0

We add all the numbers together, and all the variables

20y^2-193y-3=0

a = 20; b = -193; c = -3;
Δ = b2-4ac
Δ = -1932-4·20·(-3)
Δ = 37489
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{-(-193)-\sqrt{37489}}{2*20}=\frac{193-\sqrt{37489}}{40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-193)+\sqrt{37489}}{2*20}=\frac{193+\sqrt{37489}}{40}
$