10=8/3r-2r

Solution for 10=8/3r-2r equation:

10=8/3r-2r

We move all terms to the left:

10-(8/3r-2r)=0


Domain of the equation: 3r-2r)!=0

r∈R


We add all the numbers together, and all the variables

-(-2r+8/3r)+10=0

We get rid of parentheses

2r-8/3r+10=0

We multiply all the terms by the denominator


2r*3r+10*3r-8=0

Wy multiply elements

6r^2+30r-8=0

a = 6; b = 30; c = -8;
Δ = b2-4ac
Δ = 302-4·6·(-8)
Δ = 1092
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{273}}{2*6}=\frac{-30-2\sqrt{273}}{12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{273}}{2*6}=\frac{-30+2\sqrt{273}}{12}
$