18/d+13=6d-13

Solution for 18/d+13=6d-13 equation:

18/d+13=6d-13

We move all terms to the left:

18/d+13-(6d-13)=0


Domain of the equation: d!=0

d∈R


We get rid of parentheses

18/d-6d+13+13=0

We multiply all the terms by the denominator


-6d*d+13*d+13*d+18=0

We add all the numbers together, and all the variables

26d-6d*d+18=0

Wy multiply elements

-6d^2+26d+18=0

a = -6; b = 26; c = +18;
Δ = b2-4ac
Δ = 262-4·(-6)·18
Δ = 1108
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:

$\sqrt{\Delta}=\sqrt{1108}=\sqrt{4*277}=\sqrt{4}*\sqrt{277}=2\sqrt{277}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{277}}{2*-6}=\frac{-26-2\sqrt{277}}{-12}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{277}}{2*-6}=\frac{-26+2\sqrt{277}}{-12}
$