-10+0.5w=1/2w-10

Solution for -10+0.5w=1/2w-10 equation:

-10+0.5w=1/2w-10

We move all terms to the left:

-10+0.5w-(1/2w-10)=0


Domain of the equation: 2w-10)!=0

w∈R


We get rid of parentheses

0.5w-1/2w+10-10=0

We multiply all the terms by the denominator


(0.5w)*2w+10*2w-10*2w-1=0

We add all the numbers together, and all the variables

(+0.5w)*2w+10*2w-10*2w-1=0

We multiply parentheses

0w^2+10*2w-10*2w-1=0

Wy multiply elements

0w^2+20w-20w-1=0

We add all the numbers together, and all the variables

w^2-1=0

a = 1; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·1·(-1)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2}{2*1}=\frac{-2}{2}
=-1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2}{2*1}=\frac{2}{2}
=1
$