100b=32487/342b

Solution for 100b=32487/342b equation:

100b=32487/342b

We move all terms to the left:

100b-(32487/342b)=0


Domain of the equation: 342b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

100b-(+32487/342b)=0

We get rid of parentheses

100b-32487/342b=0

We multiply all the terms by the denominator


100b*342b-32487=0

Wy multiply elements

34200b^2-32487=0

a = 34200; b = 0; c = -32487;
Δ = b2-4ac
Δ = 02-4·34200·(-32487)
Δ = 4444221600
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:

$\sqrt{\Delta}=\sqrt{4444221600}=\sqrt{176400*25194}=\sqrt{176400}*\sqrt{25194}=420\sqrt{25194}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-420\sqrt{25194}}{2*34200}=\frac{0-420\sqrt{25194}}{68400}
=-\frac{420\sqrt{25194}}{68400}
=-\frac{7\sqrt{25194}}{1140}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+420\sqrt{25194}}{2*34200}=\frac{0+420\sqrt{25194}}{68400}
=\frac{420\sqrt{25194}}{68400}
=\frac{7\sqrt{25194}}{1140}
$