-(-4x-1)-6/5x=4/5x-1

Solution for -(-4x-1)-6/5x=4/5x-1 equation:

-(-4x-1)-6/5x=4/5x-1

We move all terms to the left:

-(-4x-1)-6/5x-(4/5x-1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 5x-1)!=0

x∈R


We get rid of parentheses

4x-6/5x-4/5x+1+1=0

We multiply all the terms by the denominator


4x*5x+1*5x+1*5x-6-4=0

We add all the numbers together, and all the variables

4x*5x+1*5x+1*5x-10=0

Wy multiply elements

20x^2+5x+5x-10=0

We add all the numbers together, and all the variables

20x^2+10x-10=0

a = 20; b = 10; c = -10;
Δ = b2-4ac
Δ = 102-4·20·(-10)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-30}{2*20}=\frac{-40}{40}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+30}{2*20}=\frac{20}{40}
=1/2
$