(1/2)r+(1/3)r=5

Solution for (1/2)r+(1/3)r=5 equation:

(1/2)r+(1/3)r=5

We move all terms to the left:

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


Domain of the equation: 2)r!=0

r!=0/1

r!=0

r∈R



Domain of the equation: 3)r!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

r^2+r^2-5=0

We add all the numbers together, and all the variables

2r^2-5=0

a = 2; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·2·(-5)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*2}=\frac{0-2\sqrt{10}}{4}
=-\frac{2\sqrt{10}}{4}
=-\frac{\sqrt{10}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*2}=\frac{0+2\sqrt{10}}{4}
=\frac{2\sqrt{10}}{4}
=\frac{\sqrt{10}}{2}
$