5y-51.2=-13+3/4y

Solution for 5y-51.2=-13+3/4y equation:

5y-51.2=-13+3/4y

We move all terms to the left:

5y-51.2-(-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)-51.2=0

We get rid of parentheses

5y-3/4y+13-51.2=0

We multiply all the terms by the denominator


5y*4y+13*4y-(51.2)*4y-3=0

We multiply parentheses

5y*4y+13*4y-204.8y-3=0

Wy multiply elements

20y^2+52y-204.8y-3=0

We add all the numbers together, and all the variables

20y^2-152.8y-3=0

a = 20; b = -152.8; c = -3;
Δ = b2-4ac
Δ = -152.82-4·20·(-3)
Δ = 23587.84
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{-(-152.8)-\sqrt{23587.84}}{2*20}=\frac{152.8-\sqrt{23587.84}}{40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-152.8)+\sqrt{23587.84}}{2*20}=\frac{152.8+\sqrt{23587.84}}{40}
$