b+1/2b+3=24

Solution for b+1/2b+3=24 equation:

b+1/2b+3=24

We move all terms to the left:

b+1/2b+3-(24)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

b+1/2b-21=0

We multiply all the terms by the denominator


b*2b-21*2b+1=0

Wy multiply elements

2b^2-42b+1=0

a = 2; b = -42; c = +1;
Δ = b2-4ac
Δ = -422-4·2·1
Δ = 1756
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:

$\sqrt{\Delta}=\sqrt{1756}=\sqrt{4*439}=\sqrt{4}*\sqrt{439}=2\sqrt{439}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{439}}{2*2}=\frac{42-2\sqrt{439}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{439}}{2*2}=\frac{42+2\sqrt{439}}{4}
$