2d+12/d=24

Solution for 2d+12/d=24 equation:

2d+12/d=24

We move all terms to the left:

2d+12/d-(24)=0


Domain of the equation: d!=0

d∈R


We multiply all the terms by the denominator


2d*d-24*d+12=0

We add all the numbers together, and all the variables

-24d+2d*d+12=0

Wy multiply elements

2d^2-24d+12=0

a = 2; b = -24; c = +12;
Δ = b2-4ac
Δ = -242-4·2·12
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{30}}{2*2}=\frac{24-4\sqrt{30}}{4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{30}}{2*2}=\frac{24+4\sqrt{30}}{4}
$