5y-5.25=13+3/4y

Solution for 5y-5.25=13+3/4y equation:

5y-5.25=13+3/4y

We move all terms to the left:

5y-5.25-(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)-5.25=0

We get rid of parentheses

5y-3/4y-13-5.25=0

We multiply all the terms by the denominator


5y*4y-13*4y-(5.25)*4y-3=0

We multiply parentheses

5y*4y-13*4y-21y-3=0

Wy multiply elements

20y^2-52y-21y-3=0

We add all the numbers together, and all the variables

20y^2-73y-3=0

a = 20; b = -73; c = -3;
Δ = b2-4ac
Δ = -732-4·20·(-3)
Δ = 5569
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{-(-73)-\sqrt{5569}}{2*20}=\frac{73-\sqrt{5569}}{40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-73)+\sqrt{5569}}{2*20}=\frac{73+\sqrt{5569}}{40}
$