4/b+5b-4=14

Solution for 4/b+5b-4=14 equation:

4/b+5b-4=14

We move all terms to the left:

4/b+5b-4-(14)=0


Domain of the equation: b!=0

b∈R


We add all the numbers together, and all the variables

5b+4/b-18=0

We multiply all the terms by the denominator


5b*b-18*b+4=0

We add all the numbers together, and all the variables

-18b+5b*b+4=0

Wy multiply elements

5b^2-18b+4=0

a = 5; b = -18; c = +4;
Δ = b2-4ac
Δ = -182-4·5·4
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{61}}{2*5}=\frac{18-2\sqrt{61}}{10}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{61}}{2*5}=\frac{18+2\sqrt{61}}{10}
$