6w=77/5w

Solution for 6w=77/5w equation:

6w=77/5w

We move all terms to the left:

6w-(77/5w)=0


Domain of the equation: 5w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

6w-(+77/5w)=0

We get rid of parentheses

6w-77/5w=0

We multiply all the terms by the denominator


6w*5w-77=0

Wy multiply elements

30w^2-77=0

a = 30; b = 0; c = -77;
Δ = b2-4ac
Δ = 02-4·30·(-77)
Δ = 9240
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:

$\sqrt{\Delta}=\sqrt{9240}=\sqrt{4*2310}=\sqrt{4}*\sqrt{2310}=2\sqrt{2310}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2310}}{2*30}=\frac{0-2\sqrt{2310}}{60}
=-\frac{2\sqrt{2310}}{60}
=-\frac{\sqrt{2310}}{30}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2310}}{2*30}=\frac{0+2\sqrt{2310}}{60}
=\frac{2\sqrt{2310}}{60}
=\frac{\sqrt{2310}}{30}
$