11/7d+d=132

Solution for 11/7d+d=132 equation:

11/7d+d=132

We move all terms to the left:

11/7d+d-(132)=0


Domain of the equation: 7d!=0

d!=0/7

d!=0

d∈R


We add all the numbers together, and all the variables

d+11/7d-132=0

We multiply all the terms by the denominator


d*7d-132*7d+11=0

Wy multiply elements

7d^2-924d+11=0

a = 7; b = -924; c = +11;
Δ = b2-4ac
Δ = -9242-4·7·11
Δ = 853468
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{853468}=\sqrt{4*213367}=\sqrt{4}*\sqrt{213367}=2\sqrt{213367}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-924)-2\sqrt{213367}}{2*7}=\frac{924-2\sqrt{213367}}{14}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-924)+2\sqrt{213367}}{2*7}=\frac{924+2\sqrt{213367}}{14}
$