363b/362b=2162-b

Solution for 363b/362b=2162-b equation:

363b/362b=2162-b

We move all terms to the left:

363b/362b-(2162-b)=0


Domain of the equation: 362b!=0

b!=0/362

b!=0

b∈R


We add all the numbers together, and all the variables

363b/362b-(-1b+2162)=0

We get rid of parentheses

363b/362b+1b-2162=0

We multiply all the terms by the denominator


363b+1b*362b-2162*362b=0

Wy multiply elements

362b^2+363b-782644b=0

We add all the numbers together, and all the variables

362b^2-782281b=0

a = 362; b = -782281; c = 0;
Δ = b2-4ac
Δ = -7822812-4·362·0
Δ = 611963562961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{611963562961}=782281$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-782281)-782281}{2*362}=\frac{0}{724}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-782281)+782281}{2*362}=\frac{1564562}{724}
=2160+361/362
$