30/b=5b

Solution for 30/b=5b equation:

30/b=5b

We move all terms to the left:

30/b-(5b)=0


Domain of the equation: b!=0

b∈R


We add all the numbers together, and all the variables

-5b+30/b=0

We multiply all the terms by the denominator


-5b*b+30=0

Wy multiply elements

-5b^2+30=0

a = -5; b = 0; c = +30;
Δ = b2-4ac
Δ = 02-4·(-5)·30
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*-5}=\frac{0-10\sqrt{6}}{-10}
=-\frac{10\sqrt{6}}{-10}
=-\frac{\sqrt{6}}{-1}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*-5}=\frac{0+10\sqrt{6}}{-10}
=\frac{10\sqrt{6}}{-10}
=\frac{\sqrt{6}}{-1}
$