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

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

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

We move all terms to the left:

2-1/2b+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-56=0

We multiply all the terms by the denominator


2b*2b-56*2b-1=0

Wy multiply elements

4b^2-112b-1=0

a = 4; b = -112; c = -1;
Δ = b2-4ac
Δ = -1122-4·4·(-1)
Δ = 12560
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:

$\sqrt{\Delta}=\sqrt{12560}=\sqrt{16*785}=\sqrt{16}*\sqrt{785}=4\sqrt{785}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-4\sqrt{785}}{2*4}=\frac{112-4\sqrt{785}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+4\sqrt{785}}{2*4}=\frac{112+4\sqrt{785}}{8}
$