(1/12)r+(1/18)r=1

Solution for (1/12)r+(1/18)r=1 equation:

(1/12)r+(1/18)r=1

We move all terms to the left:

(1/12)r+(1/18)r-(1)=0


Domain of the equation: 12)r!=0

r!=0/1

r!=0

r∈R



Domain of the equation: 18)r!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

(+1/12)r+(+1/18)r-1=0

We multiply parentheses

r^2+r^2-1=0

We add all the numbers together, and all the variables

2r^2-1=0

a = 2; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·2·(-1)
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2}}{2*2}=\frac{0-2\sqrt{2}}{4}
=-\frac{2\sqrt{2}}{4}
=-\frac{\sqrt{2}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2}}{2*2}=\frac{0+2\sqrt{2}}{4}
=\frac{2\sqrt{2}}{4}
=\frac{\sqrt{2}}{2}
$