1/3r+12/3+31/4r=67/48

Solution for 1/3r+12/3+31/4r=67/48 equation:

1/3r+12/3+31/4r=67/48

We move all terms to the left:

1/3r+12/3+31/4r-(67/48)=0


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R



Domain of the equation: 4r!=0

r!=0/4

r!=0

r∈R


We add all the numbers together, and all the variables

1/3r+31/4r+12/3-(+67/48)=0

We add all the numbers together, and all the variables

1/3r+31/4r+4-(+67/48)=0

We get rid of parentheses

1/3r+31/4r+4-67/48=0

We calculate fractions


(-3216r^2)/2304r^2+768r/2304r^2+17856r/2304r^2+4=0

We multiply all the terms by the denominator


(-3216r^2)+768r+17856r+4*2304r^2=0

We add all the numbers together, and all the variables

(-3216r^2)+18624r+4*2304r^2=0

Wy multiply elements

(-3216r^2)+9216r^2+18624r=0

We get rid of parentheses

-3216r^2+9216r^2+18624r=0

We add all the numbers together, and all the variables

6000r^2+18624r=0

a = 6000; b = 18624; c = 0;
Δ = b2-4ac
Δ = 186242-4·6000·0
Δ = 346853376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{346853376}=18624$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18624)-18624}{2*6000}=\frac{-37248}{12000}
=-3+13/125
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18624)+18624}{2*6000}=\frac{0}{12000}
=0
$