1/6w+80=7w+80

Solution for 1/6w+80=7w+80 equation:

1/6w+80=7w+80

We move all terms to the left:

1/6w+80-(7w+80)=0


Domain of the equation: 6w!=0

w!=0/6

w!=0

w∈R


We get rid of parentheses

1/6w-7w-80+80=0

We multiply all the terms by the denominator


-7w*6w-80*6w+80*6w+1=0

Wy multiply elements

-42w^2-480w+480w+1=0

We add all the numbers together, and all the variables

-42w^2+1=0

a = -42; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-42)·1
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*-42}=\frac{0-2\sqrt{42}}{-84}
=-\frac{2\sqrt{42}}{-84}
=-\frac{\sqrt{42}}{-42}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*-42}=\frac{0+2\sqrt{42}}{-84}
=\frac{2\sqrt{42}}{-84}
=\frac{\sqrt{42}}{-42}
$