(21/2)d=71/2

Solution for (21/2)d=71/2 equation:

(21/2)d=71/2

We move all terms to the left:

(21/2)d-(71/2)=0


Domain of the equation: 2)d!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

(+21/2)d-(+71/2)=0

We multiply parentheses

21d^2-(+71/2)=0

We get rid of parentheses

21d^2-71/2=0

We multiply all the terms by the denominator


21d^2*2-71=0

Wy multiply elements

42d^2-71=0

a = 42; b = 0; c = -71;
Δ = b2-4ac
Δ = 02-4·42·(-71)
Δ = 11928
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:

$\sqrt{\Delta}=\sqrt{11928}=\sqrt{4*2982}=\sqrt{4}*\sqrt{2982}=2\sqrt{2982}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2982}}{2*42}=\frac{0-2\sqrt{2982}}{84}
=-\frac{2\sqrt{2982}}{84}
=-\frac{\sqrt{2982}}{42}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2982}}{2*42}=\frac{0+2\sqrt{2982}}{84}
=\frac{2\sqrt{2982}}{84}
=\frac{\sqrt{2982}}{42}
$