1/2w+7=2w+2

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

1/2w+7=2w+2

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4w^2-4w+14w+1=0

We add all the numbers together, and all the variables

-4w^2+10w+1=0

a = -4; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-4)·1
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{29}}{2*-4}=\frac{-10-2\sqrt{29}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{29}}{2*-4}=\frac{-10+2\sqrt{29}}{-8}
$