5/3r-1/2=-8-5/6r

Solution for 5/3r-1/2=-8-5/6r equation:

5/3r-1/2=-8-5/6r

We move all terms to the left:

5/3r-1/2-(-8-5/6r)=0


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R



Domain of the equation: 6r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

5/3r-(-5/6r-8)-1/2=0

We get rid of parentheses

5/3r+5/6r+8-1/2=0

We calculate fractions


(-108r^2)/72r^2+120r/72r^2+60r/72r^2+8=0

We multiply all the terms by the denominator


(-108r^2)+120r+60r+8*72r^2=0

We add all the numbers together, and all the variables

(-108r^2)+180r+8*72r^2=0

Wy multiply elements

(-108r^2)+576r^2+180r=0

We get rid of parentheses

-108r^2+576r^2+180r=0

We add all the numbers together, and all the variables

468r^2+180r=0

a = 468; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·468·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*468}=\frac{-360}{936}
=-5/13
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*468}=\frac{0}{936}
=0
$