r+11/8r=29

Solution for r+11/8r=29 equation:

r+11/8r=29

We move all terms to the left:

r+11/8r-(29)=0


Domain of the equation: 8r!=0

r!=0/8

r!=0

r∈R


We multiply all the terms by the denominator


r*8r-29*8r+11=0

Wy multiply elements

8r^2-232r+11=0

a = 8; b = -232; c = +11;
Δ = b2-4ac
Δ = -2322-4·8·11
Δ = 53472
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:

$\sqrt{\Delta}=\sqrt{53472}=\sqrt{16*3342}=\sqrt{16}*\sqrt{3342}=4\sqrt{3342}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-232)-4\sqrt{3342}}{2*8}=\frac{232-4\sqrt{3342}}{16}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-232)+4\sqrt{3342}}{2*8}=\frac{232+4\sqrt{3342}}{16}
$