X/5x-2=4x+3

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

X/5X-2=4X+3

We move all terms to the left:

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


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-20X^2+X-15X-10X=0

We add all the numbers together, and all the variables

-20X^2-24X=0

a = -20; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·(-20)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*-20}=\frac{0}{-40}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*-20}=\frac{48}{-40}
=-1+1/5
$