22.5=d/2+d2.5725

Solution for 22.5=d/2+d2.5725 equation:

22.5=d/2+d2.5725

We move all terms to the left:

22.5-(d/2+d2.5725)=0


Domain of the equation: 2+d2.5725)!=0

We move all terms containing d to the left, all other terms to the right

d2.5725)!=-2

d!=-2/1

d!=-2

d∈R


We add all the numbers together, and all the variables

-(+d/2+d2.5725)+22.5=0

We get rid of parentheses

-d/2-d2.5725+22.5=0

We multiply all the terms by the denominator


-d-(d2.5725)*2+(22.5)*2=0

We add all the numbers together, and all the variables

-d-(+d2.5725)*2+(22.5)*2=0

We add all the numbers together, and all the variables

-1d-(+d2.5725)*2+45=0

We multiply parentheses

-2d^2-1d+45=0

a = -2; b = -1; c = +45;
Δ = b2-4ac
Δ = -12-4·(-2)·45
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-19}{2*-2}=\frac{-18}{-4}
=4+1/2
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+19}{2*-2}=\frac{20}{-4}
=-5
$