1/2w+7-6w+2=32

Solution for 1/2w+7-6w+2=32 equation:

1/2w+7-6w+2=32

We move all terms to the left:

1/2w+7-6w+2-(32)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We add all the numbers together, and all the variables

-6w+1/2w-23=0

We multiply all the terms by the denominator


-6w*2w-23*2w+1=0

Wy multiply elements

-12w^2-46w+1=0

a = -12; b = -46; c = +1;
Δ = b2-4ac
Δ = -462-4·(-12)·1
Δ = 2164
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:

$\sqrt{\Delta}=\sqrt{2164}=\sqrt{4*541}=\sqrt{4}*\sqrt{541}=2\sqrt{541}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{541}}{2*-12}=\frac{46-2\sqrt{541}}{-24}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{541}}{2*-12}=\frac{46+2\sqrt{541}}{-24}
$