r/3r-7r=32

Solution for r/3r-7r=32 equation:

r/3r-7r=32

We move all terms to the left:

r/3r-7r-(32)=0


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R


We add all the numbers together, and all the variables

-7r+r/3r-32=0

We multiply all the terms by the denominator


-7r*3r+r-32*3r=0

We add all the numbers together, and all the variables

r-7r*3r-32*3r=0

Wy multiply elements

-21r^2+r-96r=0

We add all the numbers together, and all the variables

-21r^2-95r=0

a = -21; b = -95; c = 0;
Δ = b2-4ac
Δ = -952-4·(-21)·0
Δ = 9025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9025}=95$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-95)-95}{2*-21}=\frac{0}{-42}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95)+95}{2*-21}=\frac{190}{-42}
=-4+11/21
$