-2w+4=2/5w-8

Solution for -2w+4=2/5w-8 equation:

-2w+4=2/5w-8

We move all terms to the left:

-2w+4-(2/5w-8)=0


Domain of the equation: 5w-8)!=0

w∈R


We get rid of parentheses

-2w-2/5w+8+4=0

We multiply all the terms by the denominator


-2w*5w+8*5w+4*5w-2=0

Wy multiply elements

-10w^2+40w+20w-2=0

We add all the numbers together, and all the variables

-10w^2+60w-2=0

a = -10; b = 60; c = -2;
Δ = b2-4ac
Δ = 602-4·(-10)·(-2)
Δ = 3520
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:

$\sqrt{\Delta}=\sqrt{3520}=\sqrt{64*55}=\sqrt{64}*\sqrt{55}=8\sqrt{55}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-8\sqrt{55}}{2*-10}=\frac{-60-8\sqrt{55}}{-20}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+8\sqrt{55}}{2*-10}=\frac{-60+8\sqrt{55}}{-20}
$