d-4=19/d=15

Solution for d-4=19/d=15 equation:

d-4=19/d=15

We move all terms to the left:

d-4-(19/d)=0


Domain of the equation: d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

d-(+19/d)-4=0

We get rid of parentheses

d-19/d-4=0

We multiply all the terms by the denominator


d*d-4*d-19=0

We add all the numbers together, and all the variables

-4d+d*d-19=0

Wy multiply elements

d^2-4d-19=0

a = 1; b = -4; c = -19;
Δ = b2-4ac
Δ = -42-4·1·(-19)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{23}}{2*1}=\frac{4-2\sqrt{23}}{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{23}}{2*1}=\frac{4+2\sqrt{23}}{2}
$