1/2r+1/3r=10

Solution for 1/2r+1/3r=10 equation:

1/2r+1/3r=10

We move all terms to the left:

1/2r+1/3r-(10)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R



Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R


We calculate fractions


3r/6r^2+2r/6r^2-10=0

We multiply all the terms by the denominator


3r+2r-10*6r^2=0

We add all the numbers together, and all the variables

5r-10*6r^2=0

Wy multiply elements

-60r^2+5r=0

a = -60; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-60)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-60}=\frac{-10}{-120}
=1/12
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-60}=\frac{0}{-120}
=0
$