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

-1w^2+40w-1=0

a = -1; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·(-1)·(-1)
Δ = 1596
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:

$\sqrt{\Delta}=\sqrt{1596}=\sqrt{4*399}=\sqrt{4}*\sqrt{399}=2\sqrt{399}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{399}}{2*-1}=\frac{-40-2\sqrt{399}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{399}}{2*-1}=\frac{-40+2\sqrt{399}}{-2}
$