-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}
$