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

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

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

We move all terms to the left:

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


Domain of the equation: 5x-2)!=0

x∈R


We add all the numbers together, and all the variables

-(-1x+1/5x+3)-4=0

We get rid of parentheses

1x-1/5x-3-4=0

We multiply all the terms by the denominator


1x*5x-3*5x-4*5x-1=0

Wy multiply elements

5x^2-15x-20x-1=0

We add all the numbers together, and all the variables

5x^2-35x-1=0

a = 5; b = -35; c = -1;
Δ = b2-4ac
Δ = -352-4·5·(-1)
Δ = 1245
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-\sqrt{1245}}{2*5}=\frac{35-\sqrt{1245}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1245}}{2*5}=\frac{35+\sqrt{1245}}{10}
$