1/3r-19/5-17/6r=68/15

Solution for 1/3r-19/5-17/6r=68/15 equation:

1/3r-19/5-17/6r=68/15

We move all terms to the left:

1/3r-19/5-17/6r-(68/15)=0


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R



Domain of the equation: 6r!=0

r!=0/6

r!=0

r∈R


We add all the numbers together, and all the variables

1/3r-17/6r-19/5-(+68/15)=0

We get rid of parentheses

1/3r-17/6r-19/5-68/15=0

We calculate fractions


(-30780r^2)/6750r^2+(-36720r^2)/6750r^2+2250r/6750r^2+(-19125r)/6750r^2=0

We multiply all the terms by the denominator


(-30780r^2)+(-36720r^2)+2250r+(-19125r)=0

We get rid of parentheses

-30780r^2-36720r^2+2250r-19125r=0

We add all the numbers together, and all the variables

-67500r^2-16875r=0

a = -67500; b = -16875; c = 0;
Δ = b2-4ac
Δ = -168752-4·(-67500)·0
Δ = 284765625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{284765625}=16875$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16875)-16875}{2*-67500}=\frac{0}{-135000}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16875)+16875}{2*-67500}=\frac{33750}{-135000}
=-1/4
$