3/2r+3r=11

Solution for 3/2r+3r=11 equation:

3/2r+3r=11

We move all terms to the left:

3/2r+3r-(11)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R


We add all the numbers together, and all the variables

3r+3/2r-11=0

We multiply all the terms by the denominator


3r*2r-11*2r+3=0

Wy multiply elements

6r^2-22r+3=0

a = 6; b = -22; c = +3;
Δ = b2-4ac
Δ = -222-4·6·3
Δ = 412
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:

$\sqrt{\Delta}=\sqrt{412}=\sqrt{4*103}=\sqrt{4}*\sqrt{103}=2\sqrt{103}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{103}}{2*6}=\frac{22-2\sqrt{103}}{12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{103}}{2*6}=\frac{22+2\sqrt{103}}{12}
$