1/5d=1/2d+6

Solution for 1/5d=1/2d+6 equation:

1/5d=1/2d+6

We move all terms to the left:

1/5d-(1/2d+6)=0


Domain of the equation: 5d!=0

d!=0/5

d!=0

d∈R



Domain of the equation: 2d+6)!=0

d∈R


We get rid of parentheses

1/5d-1/2d-6=0

We calculate fractions


2d/10d^2+(-5d)/10d^2-6=0

We multiply all the terms by the denominator


2d+(-5d)-6*10d^2=0

Wy multiply elements

-60d^2+2d+(-5d)=0

We get rid of parentheses

-60d^2+2d-5d=0

We add all the numbers together, and all the variables

-60d^2-3d=0

a = -60; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-60)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-60}=\frac{0}{-120}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-60}=\frac{6}{-120}
=-1/20
$