5w=7/8w

Solution for 5w=7/8w equation:

5w=7/8w

We move all terms to the left:

5w-(7/8w)=0


Domain of the equation: 8w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

5w-(+7/8w)=0

We get rid of parentheses

5w-7/8w=0

We multiply all the terms by the denominator


5w*8w-7=0

Wy multiply elements

40w^2-7=0

a = 40; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·40·(-7)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{70}}{2*40}=\frac{0-4\sqrt{70}}{80}
=-\frac{4\sqrt{70}}{80}
=-\frac{\sqrt{70}}{20}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{70}}{2*40}=\frac{0+4\sqrt{70}}{80}
=\frac{4\sqrt{70}}{80}
=\frac{\sqrt{70}}{20}
$