2/5d-d=18

Solution for 2/5d-d=18 equation:

2/5d-d=18

We move all terms to the left:

2/5d-d-(18)=0


Domain of the equation: 5d!=0

d!=0/5

d!=0

d∈R


We add all the numbers together, and all the variables

-1d+2/5d-18=0

We multiply all the terms by the denominator


-1d*5d-18*5d+2=0

Wy multiply elements

-5d^2-90d+2=0

a = -5; b = -90; c = +2;
Δ = b2-4ac
Δ = -902-4·(-5)·2
Δ = 8140
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:

$\sqrt{\Delta}=\sqrt{8140}=\sqrt{4*2035}=\sqrt{4}*\sqrt{2035}=2\sqrt{2035}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2035}}{2*-5}=\frac{90-2\sqrt{2035}}{-10}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2035}}{2*-5}=\frac{90+2\sqrt{2035}}{-10}
$