5x-19/x-4=3x/x

Solution for 5x-19/x-4=3x/x equation:

5x-19/x-4=3x/x

We move all terms to the left:

5x-19/x-4-(3x/x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-19/x-(+3x/x)-4=0

We get rid of parentheses

5x-19/x-3x/x-4=0

We multiply all the terms by the denominator


5x*x-3x-4*x-19=0

We add all the numbers together, and all the variables

-7x+5x*x-19=0

Wy multiply elements

5x^2-7x-19=0

a = 5; b = -7; c = -19;
Δ = b2-4ac
Δ = -72-4·5·(-19)
Δ = 429
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{429}}{2*5}=\frac{7-\sqrt{429}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{429}}{2*5}=\frac{7+\sqrt{429}}{10}
$