1/2w-2=-5+w

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

1/2w-2=-5+w

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We add all the numbers together, and all the variables

1/2w-(w-5)-2=0

We get rid of parentheses

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

We multiply all the terms by the denominator


-w*2w+5*2w-2*2w+1=0

Wy multiply elements

-2w^2+10w-4w+1=0

We add all the numbers together, and all the variables

-2w^2+6w+1=0

a = -2; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·(-2)·1
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{11}}{2*-2}=\frac{-6-2\sqrt{11}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{11}}{2*-2}=\frac{-6+2\sqrt{11}}{-4}
$