2/5w+6=w+9

Solution for 2/5w+6=w+9 equation:

2/5w+6=w+9

We move all terms to the left:

2/5w+6-(w+9)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R


We get rid of parentheses

2/5w-w-9+6=0

We multiply all the terms by the denominator


-w*5w-9*5w+6*5w+2=0

Wy multiply elements

-5w^2-45w+30w+2=0

We add all the numbers together, and all the variables

-5w^2-15w+2=0

a = -5; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·(-5)·2
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{265}}{2*-5}=\frac{15-\sqrt{265}}{-10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{265}}{2*-5}=\frac{15+\sqrt{265}}{-10}
$