1/5b+6=-6b+99

Solution for 1/5b+6=-6b+99 equation:

1/5b+6=-6b+99

We move all terms to the left:

1/5b+6-(-6b+99)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R


We get rid of parentheses

1/5b+6b-99+6=0

We multiply all the terms by the denominator


6b*5b-99*5b+6*5b+1=0

Wy multiply elements

30b^2-495b+30b+1=0

We add all the numbers together, and all the variables

30b^2-465b+1=0

a = 30; b = -465; c = +1;
Δ = b2-4ac
Δ = -4652-4·30·1
Δ = 216105
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{-(-465)-\sqrt{216105}}{2*30}=\frac{465-\sqrt{216105}}{60}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-465)+\sqrt{216105}}{2*30}=\frac{465+\sqrt{216105}}{60}
$