4/5y-3/4=3/10y-1

Solution for 4/5y-3/4=3/10y-1 equation:

4/5y-3/4=3/10y-1

We move all terms to the left:

4/5y-3/4-(3/10y-1)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 10y-1)!=0

y∈R


We get rid of parentheses

4/5y-3/10y+1-3/4=0

We calculate fractions


(-150y^2)/800y^2+640y/800y^2+(-240y)/800y^2+1=0

We multiply all the terms by the denominator


(-150y^2)+640y+(-240y)+1*800y^2=0

Wy multiply elements

(-150y^2)+800y^2+640y+(-240y)=0

We get rid of parentheses

-150y^2+800y^2+640y-240y=0

We add all the numbers together, and all the variables

650y^2+400y=0

a = 650; b = 400; c = 0;
Δ = b2-4ac
Δ = 4002-4·650·0
Δ = 160000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{160000}=400$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-400}{2*650}=\frac{-800}{1300}
=-8/13
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+400}{2*650}=\frac{0}{1300}
=0
$