6/5*w=5

Solution for 6/5*w=5 equation:

6/5*w=5

We move all terms to the left:

6/5*w-(5)=0


Domain of the equation: 5*w!=0

w!=0/1

w!=0

w∈R


We multiply all the terms by the denominator


-5*5*w+6=0

Wy multiply elements

-25w*w+6=0

Wy multiply elements

-25w^2+6=0

a = -25; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-25)·6
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*-25}=\frac{0-10\sqrt{6}}{-50}
=-\frac{10\sqrt{6}}{-50}
=-\frac{\sqrt{6}}{-5}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*-25}=\frac{0+10\sqrt{6}}{-50}
=\frac{10\sqrt{6}}{-50}
=\frac{\sqrt{6}}{-5}
$