2/5d+18=4d-39

Solution for 2/5d+18=4d-39 equation:

2/5d+18=4d-39

We move all terms to the left:

2/5d+18-(4d-39)=0


Domain of the equation: 5d!=0

d!=0/5

d!=0

d∈R


We get rid of parentheses

2/5d-4d+39+18=0

We multiply all the terms by the denominator


-4d*5d+39*5d+18*5d+2=0

Wy multiply elements

-20d^2+195d+90d+2=0

We add all the numbers together, and all the variables

-20d^2+285d+2=0

a = -20; b = 285; c = +2;
Δ = b2-4ac
Δ = 2852-4·(-20)·2
Δ = 81385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(285)-\sqrt{81385}}{2*-20}=\frac{-285-\sqrt{81385}}{-40}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(285)+\sqrt{81385}}{2*-20}=\frac{-285+\sqrt{81385}}{-40}
$