X/4x+1=5x-2

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

X/4X+1=5X-2

We move all terms to the left:

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


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-20X^2+X+8X+4X=0

We add all the numbers together, and all the variables

-20X^2+13X=0

a = -20; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-20)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-20}=\frac{-26}{-40}
=13/20
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-20}=\frac{0}{-40}
=0
$