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

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

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

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-20x^2+10x-25x+1=0

We add all the numbers together, and all the variables

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

a = -20; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·(-20)·1
Δ = 305
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{-(-15)-\sqrt{305}}{2*-20}=\frac{15-\sqrt{305}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{305}}{2*-20}=\frac{15+\sqrt{305}}{-40}
$