30/d-2d=6

Solution for 30/d-2d=6 equation:

30/d-2d=6

We move all terms to the left:

30/d-2d-(6)=0


Domain of the equation: d!=0

d∈R


We add all the numbers together, and all the variables

-2d+30/d-6=0

We multiply all the terms by the denominator


-2d*d-6*d+30=0

We add all the numbers together, and all the variables

-6d-2d*d+30=0

Wy multiply elements

-2d^2-6d+30=0

a = -2; b = -6; c = +30;
Δ = b2-4ac
Δ = -62-4·(-2)·30
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{69}}{2*-2}=\frac{6-2\sqrt{69}}{-4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{69}}{2*-2}=\frac{6+2\sqrt{69}}{-4}
$