7/10w-18=1/5w

Solution for 7/10w-18=1/5w equation:

7/10w-18=1/5w

We move all terms to the left:

7/10w-18-(1/5w)=0


Domain of the equation: 10w!=0

w!=0/10

w!=0

w∈R



Domain of the equation: 5w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

7/10w-(+1/5w)-18=0

We get rid of parentheses

7/10w-1/5w-18=0

We calculate fractions


35w/50w^2+(-10w)/50w^2-18=0

We multiply all the terms by the denominator


35w+(-10w)-18*50w^2=0

Wy multiply elements

-900w^2+35w+(-10w)=0

We get rid of parentheses

-900w^2+35w-10w=0

We add all the numbers together, and all the variables

-900w^2+25w=0

a = -900; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-900)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-900}=\frac{-50}{-1800}
=1/36
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-900}=\frac{0}{-1800}
=0
$