/5w-6=5w+9

Solution for /5w-6=5w+9 equation:

/5w-6=5w+9

We move all terms to the left:

/5w-6-(5w+9)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R


We get rid of parentheses

/5w-5w-9-6=0

We multiply all the terms by the denominator


-5w*5w-9*5w-6*5w+=0

We add all the numbers together, and all the variables

-5w*5w-9*5w-6*5w=0

Wy multiply elements

-25w^2-45w-30w=0

We add all the numbers together, and all the variables

-25w^2-75w=0

a = -25; b = -75; c = 0;
Δ = b2-4ac
Δ = -752-4·(-25)·0
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-75}{2*-25}=\frac{0}{-50}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+75}{2*-25}=\frac{150}{-50}
=-3
$