(5/2-b)*b=1

Solution for (5/2-b)*b=1 equation:

(5/2-b)*b=1

We move all terms to the left:

(5/2-b)*b-(1)=0


Domain of the equation: 2-b)*b!=0

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

-b)*b!=-2

b!=-2/1

b!=-2

b∈R


We add all the numbers together, and all the variables

(-1b+5/2)*b-1=0

We multiply parentheses

-1b^2+5b^2-1=0

We add all the numbers together, and all the variables

4b^2-1=0

a = 4; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·4·(-1)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*4}=\frac{-4}{8}
=-1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*4}=\frac{4}{8}
=1/2
$