1/2d-6d=5

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

1/2d-6d=5

We move all terms to the left:

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


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-6d*2d-5*2d+1=0

Wy multiply elements

-12d^2-10d+1=0

a = -12; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·(-12)·1
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{37}}{2*-12}=\frac{10-2\sqrt{37}}{-24}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{37}}{2*-12}=\frac{10+2\sqrt{37}}{-24}
$