2/5w+6(1/5w-4)=32

Solution for 2/5w+6(1/5w-4)=32 equation:

2/5w+6(1/5w-4)=32

We move all terms to the left:

2/5w+6(1/5w-4)-(32)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R



Domain of the equation: 5w-4)!=0

w∈R


We multiply parentheses

2/5w+6w-24-32=0

We multiply all the terms by the denominator


6w*5w-24*5w-32*5w+2=0

Wy multiply elements

30w^2-120w-160w+2=0

We add all the numbers together, and all the variables

30w^2-280w+2=0

a = 30; b = -280; c = +2;
Δ = b2-4ac
Δ = -2802-4·30·2
Δ = 78160
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:

$\sqrt{\Delta}=\sqrt{78160}=\sqrt{16*4885}=\sqrt{16}*\sqrt{4885}=4\sqrt{4885}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-4\sqrt{4885}}{2*30}=\frac{280-4\sqrt{4885}}{60}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+4\sqrt{4885}}{2*30}=\frac{280+4\sqrt{4885}}{60}
$