4/5b+b=27

Solution for 4/5b+b=27 equation:

4/5b+b=27

We move all terms to the left:

4/5b+b-(27)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R


We add all the numbers together, and all the variables

b+4/5b-27=0

We multiply all the terms by the denominator


b*5b-27*5b+4=0

Wy multiply elements

5b^2-135b+4=0

a = 5; b = -135; c = +4;
Δ = b2-4ac
Δ = -1352-4·5·4
Δ = 18145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-\sqrt{18145}}{2*5}=\frac{135-\sqrt{18145}}{10}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+\sqrt{18145}}{2*5}=\frac{135+\sqrt{18145}}{10}
$