10+.5w=1/2w-10

Solution for 10+.5w=1/2w-10 equation:

10+.5w=1/2w-10

We move all terms to the left:

10+.5w-(1/2w-10)=0


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

w∈R


We get rid of parentheses

.5w-1/2w+10+10=0

We multiply all the terms by the denominator


(.5w)*2w+10*2w+10*2w-1=0

We add all the numbers together, and all the variables

(+.5w)*2w+10*2w+10*2w-1=0

We multiply parentheses

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

Wy multiply elements

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

We add all the numbers together, and all the variables

2w^2+40w-1=0

a = 2; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·2·(-1)
Δ = 1608
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:

$\sqrt{\Delta}=\sqrt{1608}=\sqrt{4*402}=\sqrt{4}*\sqrt{402}=2\sqrt{402}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{402}}{2*2}=\frac{-40-2\sqrt{402}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{402}}{2*2}=\frac{-40+2\sqrt{402}}{4}
$