1/5x-40=2x-4

Solution for 1/5x-40=2x-4 equation:

1/5x-40=2x-4

We move all terms to the left:

1/5x-40-(2x-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-2x+4-40=0

We multiply all the terms by the denominator


-2x*5x+4*5x-40*5x+1=0

Wy multiply elements

-10x^2+20x-200x+1=0

We add all the numbers together, and all the variables

-10x^2-180x+1=0

a = -10; b = -180; c = +1;
Δ = b2-4ac
Δ = -1802-4·(-10)·1
Δ = 32440
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:

$\sqrt{\Delta}=\sqrt{32440}=\sqrt{4*8110}=\sqrt{4}*\sqrt{8110}=2\sqrt{8110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-2\sqrt{8110}}{2*-10}=\frac{180-2\sqrt{8110}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+2\sqrt{8110}}{2*-10}=\frac{180+2\sqrt{8110}}{-20}
$