(-5x-1)/4-(3x^2-x)/x=5

Solution for (-5x-1)/4-(3x^2-x)/x=5 equation:

(-5x-1)/4-(3x^2-x)/x=5

We move all terms to the left:

(-5x-1)/4-(3x^2-x)/x-(5)=0


Domain of the equation: x!=0

x∈R


We calculate fractions


(-5x^2-1x)/4x+(-12x^2+4x)/4x-5=0

We multiply all the terms by the denominator


(-5x^2-1x)+(-12x^2+4x)-5*4x=0

Wy multiply elements

(-5x^2-1x)+(-12x^2+4x)-20x=0

We get rid of parentheses

-5x^2-12x^2-1x+4x-20x=0

We add all the numbers together, and all the variables

-17x^2-17x=0

a = -17; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·(-17)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*-17}=\frac{0}{-34}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*-17}=\frac{34}{-34}
=-1
$