w-1/2w+4=12

Solution for w-1/2w+4=12 equation:

w-1/2w+4=12

We move all terms to the left:

w-1/2w+4-(12)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We add all the numbers together, and all the variables

w-1/2w-8=0

We multiply all the terms by the denominator


w*2w-8*2w-1=0

Wy multiply elements

2w^2-16w-1=0

a = 2; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·2·(-1)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{66}}{2*2}=\frac{16-2\sqrt{66}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{66}}{2*2}=\frac{16+2\sqrt{66}}{4}
$