10/b-b=5

Solution for 10/b-b=5 equation:

10/b-b=5

We move all terms to the left:

10/b-b-(5)=0


Domain of the equation: b!=0

b∈R


We add all the numbers together, and all the variables

-1b+10/b-5=0

We multiply all the terms by the denominator


-1b*b-5*b+10=0

We add all the numbers together, and all the variables

-5b-1b*b+10=0

Wy multiply elements

-1b^2-5b+10=0

a = -1; b = -5; c = +10;
Δ = b2-4ac
Δ = -52-4·(-1)·10
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{65}}{2*-1}=\frac{5-\sqrt{65}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{65}}{2*-1}=\frac{5+\sqrt{65}}{-2}
$