1/2r+3r=14

Solution for 1/2r+3r=14 equation:

1/2r+3r=14

We move all terms to the left:

1/2r+3r-(14)=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+1/2r-14=0

We multiply all the terms by the denominator


3r*2r-14*2r+1=0

Wy multiply elements

6r^2-28r+1=0

a = 6; b = -28; c = +1;
Δ = b2-4ac
Δ = -282-4·6·1
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{190}}{2*6}=\frac{28-2\sqrt{190}}{12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{190}}{2*6}=\frac{28+2\sqrt{190}}{12}
$