X/4x-19=x+5/4x-1

Solution for X/4x-19=x+5/4x-1 equation:

X/4X-19=X+5/4X-1

We move all terms to the left:

X/4X-19-(X+5/4X-1)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R



Domain of the equation: 4X-1)!=0

X∈R


We get rid of parentheses

X/4X-X-5/4X+1-19=0

We multiply all the terms by the denominator


X-X*4X+1*4X-19*4X-5=0

Wy multiply elements

-4X^2+X+4X-76X-5=0

We add all the numbers together, and all the variables

-4X^2-71X-5=0

a = -4; b = -71; c = -5;
Δ = b2-4ac
Δ = -712-4·(-4)·(-5)
Δ = 4961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4961}=\sqrt{121*41}=\sqrt{121}*\sqrt{41}=11\sqrt{41}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-71)-11\sqrt{41}}{2*-4}=\frac{71-11\sqrt{41}}{-8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+11\sqrt{41}}{2*-4}=\frac{71+11\sqrt{41}}{-8}
$