(7+w)-(w+7)/w=-4

Solution for (7+w)-(w+7)/w=-4 equation:

(7+w)-(w+7)/w=-4

We move all terms to the left:

(7+w)-(w+7)/w-(-4)=0


Domain of the equation: w!=0

w∈R


We add all the numbers together, and all the variables

(w+7)-(w+7)/w-(-4)=0

We add all the numbers together, and all the variables

(w+7)-(w+7)/w+4=0

We get rid of parentheses

w-(w+7)/w+7+4=0

We multiply all the terms by the denominator


w*w-(w+7)+7*w+4*w=0

We add all the numbers together, and all the variables

11w+w*w-(w+7)=0

Wy multiply elements

w^2+11w-(w+7)=0

We get rid of parentheses

w^2+11w-w-7=0

We add all the numbers together, and all the variables

w^2+10w-7=0

a = 1; b = 10; c = -7;
Δ = b2-4ac
Δ = 102-4·1·(-7)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-8\sqrt{2}}{2*1}=\frac{-10-8\sqrt{2}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+8\sqrt{2}}{2*1}=\frac{-10+8\sqrt{2}}{2}
$