/5x-2=3+4x

Solution for /5x-2=3+4x equation:

/5x-2=3+4x

We move all terms to the left:

/5x-2-(3+4x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

/5x-(4x+3)-2=0

We get rid of parentheses

/5x-4x-3-2=0

We multiply all the terms by the denominator


-4x*5x-3*5x-2*5x+=0

We add all the numbers together, and all the variables

-4x*5x-3*5x-2*5x=0

Wy multiply elements

-20x^2-15x-10x=0

We add all the numbers together, and all the variables

-20x^2-25x=0

a = -20; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·(-20)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*-20}=\frac{0}{-40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*-20}=\frac{50}{-40}
=-1+1/4
$