201=5(1+6b)2b

Solution for 201=5(1+6b)2b equation:

201=5(1+6b)2b

We move all terms to the left:

201-(5(1+6b)2b)=0

We add all the numbers together, and all the variables

-(5(6b+1)2b)+201=0


We calculate terms in parentheses: -(5(6b+1)2b), so:

5(6b+1)2b

We multiply parentheses

60b^2+10b

Back to the equation:

-(60b^2+10b)


We get rid of parentheses

-60b^2-10b+201=0

a = -60; b = -10; c = +201;
Δ = b2-4ac
Δ = -102-4·(-60)·201
Δ = 48340
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:

$\sqrt{\Delta}=\sqrt{48340}=\sqrt{4*12085}=\sqrt{4}*\sqrt{12085}=2\sqrt{12085}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{12085}}{2*-60}=\frac{10-2\sqrt{12085}}{-120}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{12085}}{2*-60}=\frac{10+2\sqrt{12085}}{-120}
$