x-2/5x-40-2/5x=60

Solution for x-2/5x-40-2/5x=60 equation:

x-2/5x-40-2/5x=60

We move all terms to the left:

x-2/5x-40-2/5x-(60)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x-2/5x-2/5x-100=0

We multiply all the terms by the denominator


x*5x-100*5x-2-2=0

We add all the numbers together, and all the variables

x*5x-100*5x-4=0

Wy multiply elements

5x^2-500x-4=0

a = 5; b = -500; c = -4;
Δ = b2-4ac
Δ = -5002-4·5·(-4)
Δ = 250080
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:

$\sqrt{\Delta}=\sqrt{250080}=\sqrt{16*15630}=\sqrt{16}*\sqrt{15630}=4\sqrt{15630}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-4\sqrt{15630}}{2*5}=\frac{500-4\sqrt{15630}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+4\sqrt{15630}}{2*5}=\frac{500+4\sqrt{15630}}{10}
$