3-7w-11=4/7w

Solution for 3-7w-11=4/7w equation:

3-7w-11=4/7w

We move all terms to the left:

3-7w-11-(4/7w)=0


Domain of the equation: 7w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

-7w-(+4/7w)+3-11=0

We add all the numbers together, and all the variables

-7w-(+4/7w)-8=0

We get rid of parentheses

-7w-4/7w-8=0

We multiply all the terms by the denominator


-7w*7w-8*7w-4=0

Wy multiply elements

-49w^2-56w-4=0

a = -49; b = -56; c = -4;
Δ = b2-4ac
Δ = -562-4·(-49)·(-4)
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-28\sqrt{3}}{2*-49}=\frac{56-28\sqrt{3}}{-98}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+28\sqrt{3}}{2*-49}=\frac{56+28\sqrt{3}}{-98}
$