4/5y-1/2y=6

Solution for 4/5y-1/2y=6 equation:

4/5y-1/2y=6

We move all terms to the left:

4/5y-1/2y-(6)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We calculate fractions


8y/10y^2+(-5y)/10y^2-6=0

We multiply all the terms by the denominator


8y+(-5y)-6*10y^2=0

Wy multiply elements

-60y^2+8y+(-5y)=0

We get rid of parentheses

-60y^2+8y-5y=0

We add all the numbers together, and all the variables

-60y^2+3y=0

a = -60; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-60)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-60}=\frac{-6}{-120}
=1/20
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-60}=\frac{0}{-120}
=0
$