1/2w+7=2w-w

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

1/2w+7=2w-w

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/2w-w+7=0

We multiply all the terms by the denominator


-w*2w+7*2w+1=0

Wy multiply elements

-2w^2+14w+1=0

a = -2; b = 14; c = +1;
Δ = b2-4ac
Δ = 142-4·(-2)·1
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{51}}{2*-2}=\frac{-14-2\sqrt{51}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{51}}{2*-2}=\frac{-14+2\sqrt{51}}{-4}
$