(41/4)d=71/2

Solution for (41/4)d=71/2 equation:

(41/4)d=71/2

We move all terms to the left:

(41/4)d-(71/2)=0


Domain of the equation: 4)d!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

(+41/4)d-(+71/2)=0

We multiply parentheses

41d^2-(+71/2)=0

We get rid of parentheses

41d^2-71/2=0

We multiply all the terms by the denominator


41d^2*2-71=0

Wy multiply elements

82d^2-71=0

a = 82; b = 0; c = -71;
Δ = b2-4ac
Δ = 02-4·82·(-71)
Δ = 23288
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:

$\sqrt{\Delta}=\sqrt{23288}=\sqrt{4*5822}=\sqrt{4}*\sqrt{5822}=2\sqrt{5822}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5822}}{2*82}=\frac{0-2\sqrt{5822}}{164}
=-\frac{2\sqrt{5822}}{164}
=-\frac{\sqrt{5822}}{82}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5822}}{2*82}=\frac{0+2\sqrt{5822}}{164}
=\frac{2\sqrt{5822}}{164}
=\frac{\sqrt{5822}}{82}
$