-1/5x+20=-x+4

Solution for -1/5x+20=-x+4 equation:

-1/5x+20=-x+4

We move all terms to the left:

-1/5x+20-(-x+4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1/5x-(-1x+4)+20=0

We get rid of parentheses

-1/5x+1x-4+20=0

We multiply all the terms by the denominator


1x*5x-4*5x+20*5x-1=0

Wy multiply elements

5x^2-20x+100x-1=0

We add all the numbers together, and all the variables

5x^2+80x-1=0

a = 5; b = 80; c = -1;
Δ = b2-4ac
Δ = 802-4·5·(-1)
Δ = 6420
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:

$\sqrt{\Delta}=\sqrt{6420}=\sqrt{4*1605}=\sqrt{4}*\sqrt{1605}=2\sqrt{1605}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-2\sqrt{1605}}{2*5}=\frac{-80-2\sqrt{1605}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+2\sqrt{1605}}{2*5}=\frac{-80+2\sqrt{1605}}{10}
$