1/2b-2+b+b=60

Solution for 1/2b-2+b+b=60 equation:

1/2b-2+b+b=60

We move all terms to the left:

1/2b-2+b+b-(60)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

2b+1/2b-62=0

We multiply all the terms by the denominator


2b*2b-62*2b+1=0

Wy multiply elements

4b^2-124b+1=0

a = 4; b = -124; c = +1;
Δ = b2-4ac
Δ = -1242-4·4·1
Δ = 15360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{15360}=\sqrt{1024*15}=\sqrt{1024}*\sqrt{15}=32\sqrt{15}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-124)-32\sqrt{15}}{2*4}=\frac{124-32\sqrt{15}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-124)+32\sqrt{15}}{2*4}=\frac{124+32\sqrt{15}}{8}
$