2/5y+11/20y+4/3=13/12

Solution for 2/5y+11/20y+4/3=13/12 equation:

2/5y+11/20y+4/3=13/12

We move all terms to the left:

2/5y+11/20y+4/3-(13/12)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 20y!=0

y!=0/20

y!=0

y∈R


We add all the numbers together, and all the variables

2/5y+11/20y+4/3-(+13/12)=0

We get rid of parentheses

2/5y+11/20y+4/3-13/12=0

We calculate fractions


(-7800y^2)/10800y^2+9600y^2/10800y^2+4320y/10800y^2+5940y/10800y^2=0

We multiply all the terms by the denominator


(-7800y^2)+9600y^2+4320y+5940y=0

We add all the numbers together, and all the variables

9600y^2+(-7800y^2)+10260y=0

We get rid of parentheses

9600y^2-7800y^2+10260y=0

We add all the numbers together, and all the variables

1800y^2+10260y=0

a = 1800; b = 10260; c = 0;
Δ = b2-4ac
Δ = 102602-4·1800·0
Δ = 105267600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{105267600}=10260$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10260)-10260}{2*1800}=\frac{-20520}{3600}
=-5+7/10
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10260)+10260}{2*1800}=\frac{0}{3600}
=0
$