2/3r-12-1/5r=3

Solution for 2/3r-12-1/5r=3 equation:

2/3r-12-1/5r=3

We move all terms to the left:

2/3r-12-1/5r-(3)=0


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R



Domain of the equation: 5r!=0

r!=0/5

r!=0

r∈R


We add all the numbers together, and all the variables

2/3r-1/5r-15=0

We calculate fractions


10r/15r^2+(-3r)/15r^2-15=0

We multiply all the terms by the denominator


10r+(-3r)-15*15r^2=0

Wy multiply elements

-225r^2+10r+(-3r)=0

We get rid of parentheses

-225r^2+10r-3r=0

We add all the numbers together, and all the variables

-225r^2+7r=0

a = -225; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-225)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-225}=\frac{-14}{-450}
=7/225
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-225}=\frac{0}{-450}
=0
$