2/5x-4=2x

Solution for 2/5x-4=2x equation:

2/5x-4=2x

We move all terms to the left:

2/5x-4-(2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+2/5x-4=0

We multiply all the terms by the denominator


-2x*5x-4*5x+2=0

Wy multiply elements

-10x^2-20x+2=0

a = -10; b = -20; c = +2;
Δ = b2-4ac
Δ = -202-4·(-10)·2
Δ = 480
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{30}}{2*-10}=\frac{20-4\sqrt{30}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{30}}{2*-10}=\frac{20+4\sqrt{30}}{-20}
$