1/6b-6b-5+5b=20

Solution for 1/6b-6b-5+5b=20 equation:

1/6b-6b-5+5b=20

We move all terms to the left:

1/6b-6b-5+5b-(20)=0


Domain of the equation: 6b!=0

b!=0/6

b!=0

b∈R


We add all the numbers together, and all the variables

-1b+1/6b-25=0

We multiply all the terms by the denominator


-1b*6b-25*6b+1=0

Wy multiply elements

-6b^2-150b+1=0

a = -6; b = -150; c = +1;
Δ = b2-4ac
Δ = -1502-4·(-6)·1
Δ = 22524
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:

$\sqrt{\Delta}=\sqrt{22524}=\sqrt{4*5631}=\sqrt{4}*\sqrt{5631}=2\sqrt{5631}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5631}}{2*-6}=\frac{150-2\sqrt{5631}}{-12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5631}}{2*-6}=\frac{150+2\sqrt{5631}}{-12}
$