7w=87/w=12

Solution for 7w=87/w=12 equation:

7w=87/w=12

We move all terms to the left:

7w-(87/w)=0


Domain of the equation: w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

7w-(+87/w)=0

We get rid of parentheses

7w-87/w=0

We multiply all the terms by the denominator


7w*w-87=0

Wy multiply elements

7w^2-87=0

a = 7; b = 0; c = -87;
Δ = b2-4ac
Δ = 02-4·7·(-87)
Δ = 2436
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:

$\sqrt{\Delta}=\sqrt{2436}=\sqrt{4*609}=\sqrt{4}*\sqrt{609}=2\sqrt{609}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{609}}{2*7}=\frac{0-2\sqrt{609}}{14}
=-\frac{2\sqrt{609}}{14}
=-\frac{\sqrt{609}}{7}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{609}}{2*7}=\frac{0+2\sqrt{609}}{14}
=\frac{2\sqrt{609}}{14}
=\frac{\sqrt{609}}{7}
$