1/8d-6=5d-45

Solution for 1/8d-6=5d-45 equation:

1/8d-6=5d-45

We move all terms to the left:

1/8d-6-(5d-45)=0


Domain of the equation: 8d!=0

d!=0/8

d!=0

d∈R


We get rid of parentheses

1/8d-5d+45-6=0

We multiply all the terms by the denominator


-5d*8d+45*8d-6*8d+1=0

Wy multiply elements

-40d^2+360d-48d+1=0

We add all the numbers together, and all the variables

-40d^2+312d+1=0

a = -40; b = 312; c = +1;
Δ = b2-4ac
Δ = 3122-4·(-40)·1
Δ = 97504
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:

$\sqrt{\Delta}=\sqrt{97504}=\sqrt{16*6094}=\sqrt{16}*\sqrt{6094}=4\sqrt{6094}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(312)-4\sqrt{6094}}{2*-40}=\frac{-312-4\sqrt{6094}}{-80}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(312)+4\sqrt{6094}}{2*-40}=\frac{-312+4\sqrt{6094}}{-80}
$