9/10a+11/15a-5/12=1/6

Solution for 9/10a+11/15a-5/12=1/6 equation:

9/10a+11/15a-5/12=1/6

We move all terms to the left:

9/10a+11/15a-5/12-(1/6)=0


Domain of the equation: 10a!=0

a!=0/10

a!=0

a∈R



Domain of the equation: 15a!=0

a!=0/15

a!=0

a∈R


We add all the numbers together, and all the variables

9/10a+11/15a-5/12-(+1/6)=0

We get rid of parentheses

9/10a+11/15a-5/12-1/6=0

We calculate fractions


(-4500a^2)/10800a^2+(-1800a^2)/10800a^2+9720a/10800a^2+7920a/10800a^2=0

We multiply all the terms by the denominator


(-4500a^2)+(-1800a^2)+9720a+7920a=0

We add all the numbers together, and all the variables

(-4500a^2)+(-1800a^2)+17640a=0

We get rid of parentheses

-4500a^2-1800a^2+17640a=0

We add all the numbers together, and all the variables

-6300a^2+17640a=0

a = -6300; b = 17640; c = 0;
Δ = b2-4ac
Δ = 176402-4·(-6300)·0
Δ = 311169600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{311169600}=17640$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17640)-17640}{2*-6300}=\frac{-35280}{-12600}
=2+4/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17640)+17640}{2*-6300}=\frac{0}{-12600}
=0
$