-11/6r-5/3r=-14

Solution for -11/6r-5/3r=-14 equation:

-11/6r-5/3r=-14

We move all terms to the left:

-11/6r-5/3r-(-14)=0


Domain of the equation: 6r!=0

r!=0/6

r!=0

r∈R



Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R


We add all the numbers together, and all the variables

-11/6r-5/3r+14=0

We calculate fractions


(-33r)/18r^2+(-30r)/18r^2+14=0

We multiply all the terms by the denominator


(-33r)+(-30r)+14*18r^2=0

Wy multiply elements

252r^2+(-33r)+(-30r)=0

We get rid of parentheses

252r^2-33r-30r=0

We add all the numbers together, and all the variables

252r^2-63r=0

a = 252; b = -63; c = 0;
Δ = b2-4ac
Δ = -632-4·252·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-63}{2*252}=\frac{0}{504}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+63}{2*252}=\frac{126}{504}
=1/4
$