6/b-1/2b=5

Solution for 6/b-1/2b=5 equation:

6/b-1/2b=5

We move all terms to the left:

6/b-1/2b-(5)=0


Domain of the equation: b!=0

b∈R



Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We calculate fractions


12b/2b^2+(-b)/2b^2-5=0

We add all the numbers together, and all the variables

12b/2b^2+(-1b)/2b^2-5=0

We multiply all the terms by the denominator


12b+(-1b)-5*2b^2=0

Wy multiply elements

-10b^2+12b+(-1b)=0

We get rid of parentheses

-10b^2+12b-1b=0

We add all the numbers together, and all the variables

-10b^2+11b=0

a = -10; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-10)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-10}=\frac{-22}{-20}
=1+1/10
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-10}=\frac{0}{-20}
=0
$