4b+5=1+5/b

Solution for 4b+5=1+5/b equation:

4b+5=1+5/b

We move all terms to the left:

4b+5-(1+5/b)=0


Domain of the equation: b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

4b-(5/b+1)+5=0

We get rid of parentheses

4b-5/b-1+5=0

We multiply all the terms by the denominator


4b*b-1*b+5*b-5=0

We add all the numbers together, and all the variables

4b+4b*b-5=0

Wy multiply elements

4b^2+4b-5=0

a = 4; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·4·(-5)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{6}}{2*4}=\frac{-4-4\sqrt{6}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{6}}{2*4}=\frac{-4+4\sqrt{6}}{8}
$