-1/2w+1=-9w-6

Solution for -1/2w+1=-9w-6 equation:

-1/2w+1=-9w-6

We move all terms to the left:

-1/2w+1-(-9w-6)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We get rid of parentheses

-1/2w+9w+6+1=0

We multiply all the terms by the denominator


9w*2w+6*2w+1*2w-1=0

Wy multiply elements

18w^2+12w+2w-1=0

We add all the numbers together, and all the variables

18w^2+14w-1=0

a = 18; b = 14; c = -1;
Δ = b2-4ac
Δ = 142-4·18·(-1)
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{67}}{2*18}=\frac{-14-2\sqrt{67}}{36}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{67}}{2*18}=\frac{-14+2\sqrt{67}}{36}
$