(1/5)d-1=12

Solution for (1/5)d-1=12 equation:

(1/5)d-1=12

We move all terms to the left:

(1/5)d-1-(12)=0


Domain of the equation: 5)d!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

(+1/5)d-1-12=0

We add all the numbers together, and all the variables

(+1/5)d-13=0

We multiply parentheses

d^2-13=0

a = 1; b = 0; c = -13;
Δ = b2-4ac
Δ = 02-4·1·(-13)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{13}}{2*1}=\frac{0-2\sqrt{13}}{2}
=-\frac{2\sqrt{13}}{2}
=-\sqrt{13}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{13}}{2*1}=\frac{0+2\sqrt{13}}{2}
=\frac{2\sqrt{13}}{2}
=\sqrt{13}
$