7/10w-18=26/1w

Solution for 7/10w-18=26/1w equation:

7/10w-18=26/1w

We move all terms to the left:

7/10w-18-(26/1w)=0


Domain of the equation: 10w!=0

w!=0/10

w!=0

w∈R



Domain of the equation: 1w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

7/10w-(+26/1w)-18=0

We get rid of parentheses

7/10w-26/1w-18=0

We calculate fractions


7w/10w^2+(-260w)/10w^2-18=0

We multiply all the terms by the denominator


7w+(-260w)-18*10w^2=0

Wy multiply elements

-180w^2+7w+(-260w)=0

We get rid of parentheses

-180w^2+7w-260w=0

We add all the numbers together, and all the variables

-180w^2-253w=0

a = -180; b = -253; c = 0;
Δ = b2-4ac
Δ = -2532-4·(-180)·0
Δ = 64009
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64009}=253$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-253)-253}{2*-180}=\frac{0}{-360}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-253)+253}{2*-180}=\frac{506}{-360}
=-1+73/180
$