4y-1/5y=0.75

Solution for 4y-1/5y=0.75 equation:

4y-1/5y=0.75

We move all terms to the left:

4y-1/5y-(0.75)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

4y-1/5y-0.75=0

We multiply all the terms by the denominator


4y*5y-(0.75)*5y-1=0

We multiply parentheses

4y*5y-3.75y-1=0

Wy multiply elements

20y^2-3.75y-1=0

a = 20; b = -3.75; c = -1;
Δ = b2-4ac
Δ = -3.752-4·20·(-1)
Δ = 94.0625
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{-(-3.75)-\sqrt{94.0625}}{2*20}=\frac{3.75-\sqrt{94.0625}}{40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.75)+\sqrt{94.0625}}{2*20}=\frac{3.75+\sqrt{94.0625}}{40}
$