1/2b=13.b=

Solution for 1/2b=13.b= equation:

1/2b=13.b=

We move all terms to the left:

1/2b-(13.b)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

1/2b-(+13.b)=0

We get rid of parentheses

1/2b-13.b=0

We multiply all the terms by the denominator


-(13.b)*2b+1=0

We add all the numbers together, and all the variables

-(+13.b)*2b+1=0

We multiply parentheses

-26b^2+1=0

a = -26; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-26)·1
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{26}}{2*-26}=\frac{0-2\sqrt{26}}{-52}
=-\frac{2\sqrt{26}}{-52}
=-\frac{\sqrt{26}}{-26}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{26}}{2*-26}=\frac{0+2\sqrt{26}}{-52}
=\frac{2\sqrt{26}}{-52}
=\frac{\sqrt{26}}{-26}
$