13=w-14/2w=

Solution for 13=w-14/2w= equation:

13=w-14/2w=

We move all terms to the left:

13-(w-14/2w)=0


Domain of the equation: 2w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

-(+w-14/2w)+13=0

We get rid of parentheses

-w+14/2w+13=0

We multiply all the terms by the denominator


-w*2w+13*2w+14=0

Wy multiply elements

-2w^2+26w+14=0

a = -2; b = 26; c = +14;
Δ = b2-4ac
Δ = 262-4·(-2)·14
Δ = 788
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{788}=\sqrt{4*197}=\sqrt{4}*\sqrt{197}=2\sqrt{197}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{197}}{2*-2}=\frac{-26-2\sqrt{197}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{197}}{2*-2}=\frac{-26+2\sqrt{197}}{-4}
$