420=b+1/6b

Solution for 420=b+1/6b equation:

420=b+1/6b

We move all terms to the left:

420-(b+1/6b)=0


Domain of the equation: 6b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

-(+b+1/6b)+420=0

We get rid of parentheses

-b-1/6b+420=0

We multiply all the terms by the denominator


-b*6b+420*6b-1=0

Wy multiply elements

-6b^2+2520b-1=0

a = -6; b = 2520; c = -1;
Δ = b2-4ac
Δ = 25202-4·(-6)·(-1)
Δ = 6350376
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:

$\sqrt{\Delta}=\sqrt{6350376}=\sqrt{4*1587594}=\sqrt{4}*\sqrt{1587594}=2\sqrt{1587594}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2520)-2\sqrt{1587594}}{2*-6}=\frac{-2520-2\sqrt{1587594}}{-12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2520)+2\sqrt{1587594}}{2*-6}=\frac{-2520+2\sqrt{1587594}}{-12}
$