3w-9=1/2w+16

Solution for 3w-9=1/2w+16 equation:

3w-9=1/2w+16

We move all terms to the left:

3w-9-(1/2w+16)=0


Domain of the equation: 2w+16)!=0

w∈R


We get rid of parentheses

3w-1/2w-16-9=0

We multiply all the terms by the denominator


3w*2w-16*2w-9*2w-1=0

Wy multiply elements

6w^2-32w-18w-1=0

We add all the numbers together, and all the variables

6w^2-50w-1=0

a = 6; b = -50; c = -1;
Δ = b2-4ac
Δ = -502-4·6·(-1)
Δ = 2524
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:

$\sqrt{\Delta}=\sqrt{2524}=\sqrt{4*631}=\sqrt{4}*\sqrt{631}=2\sqrt{631}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{631}}{2*6}=\frac{50-2\sqrt{631}}{12}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{631}}{2*6}=\frac{50+2\sqrt{631}}{12}
$