7/10w-18=5.2w

Solution for 7/10w-18=5.2w equation:

7/10w-18=5.2w

We move all terms to the left:

7/10w-18-(5.2w)=0


Domain of the equation: 10w!=0

w!=0/10

w!=0

w∈R


We add all the numbers together, and all the variables

7/10w-(+5.2w)-18=0

We get rid of parentheses

7/10w-5.2w-18=0

We multiply all the terms by the denominator


-(5.2w)*10w-18*10w+7=0

We add all the numbers together, and all the variables

-(+5.2w)*10w-18*10w+7=0

We multiply parentheses

-50w^2-18*10w+7=0

Wy multiply elements

-50w^2-180w+7=0

a = -50; b = -180; c = +7;
Δ = b2-4ac
Δ = -1802-4·(-50)·7
Δ = 33800
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:

$\sqrt{\Delta}=\sqrt{33800}=\sqrt{16900*2}=\sqrt{16900}*\sqrt{2}=130\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-130\sqrt{2}}{2*-50}=\frac{180-130\sqrt{2}}{-100}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+130\sqrt{2}}{2*-50}=\frac{180+130\sqrt{2}}{-100}
$