2/3b=15b

Solution for 2/3b=15b equation:

2/3b=15b

We move all terms to the left:

2/3b-(15b)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

-15b+2/3b=0

We multiply all the terms by the denominator


-15b*3b+2=0

Wy multiply elements

-45b^2+2=0

a = -45; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-45)·2
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10}}{2*-45}=\frac{0-6\sqrt{10}}{-90}
=-\frac{6\sqrt{10}}{-90}
=-\frac{\sqrt{10}}{-15}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*-45}=\frac{0+6\sqrt{10}}{-90}
=\frac{6\sqrt{10}}{-90}
=\frac{\sqrt{10}}{-15}
$