5y-51.25=13+3/4y

Solution for 5y-51.25=13+3/4y equation:

5y-51.25=13+3/4y

We move all terms to the left:

5y-51.25-(13+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+13)-51.25=0

We get rid of parentheses

5y-3/4y-13-51.25=0

We multiply all the terms by the denominator


5y*4y-13*4y-(51.25)*4y-3=0

We multiply parentheses

5y*4y-13*4y-205y-3=0

Wy multiply elements

20y^2-52y-205y-3=0

We add all the numbers together, and all the variables

20y^2-257y-3=0

a = 20; b = -257; c = -3;
Δ = b2-4ac
Δ = -2572-4·20·(-3)
Δ = 66289
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{-(-257)-\sqrt{66289}}{2*20}=\frac{257-\sqrt{66289}}{40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-257)+\sqrt{66289}}{2*20}=\frac{257+\sqrt{66289}}{40}
$