8=3/2w-2w-12+8

Solution for 8=3/2w-2w-12+8 equation:

8=3/2w-2w-12+8

We move all terms to the left:

8-(3/2w-2w-12+8)=0


Domain of the equation: 2w-2w-12+8)!=0

We move all terms containing w to the left, all other terms to the right

2w-2w+8)!=12

w∈R


We add all the numbers together, and all the variables

-(-2w+3/2w-4)+8=0

We get rid of parentheses

2w-3/2w+4+8=0

We multiply all the terms by the denominator


2w*2w+4*2w+8*2w-3=0

Wy multiply elements

4w^2+8w+16w-3=0

We add all the numbers together, and all the variables

4w^2+24w-3=0

a = 4; b = 24; c = -3;
Δ = b2-4ac
Δ = 242-4·4·(-3)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{39}}{2*4}=\frac{-24-4\sqrt{39}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{39}}{2*4}=\frac{-24+4\sqrt{39}}{8}
$