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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-900w^2+35w+(-50w)=0

We get rid of parentheses

-900w^2+35w-50w=0

We add all the numbers together, and all the variables

-900w^2-15w=0

a = -900; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-900)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-900}=\frac{0}{-1800}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-900}=\frac{30}{-1800}
=-1/60
$