-3/4x-20+2=3/x-5

Solution for -3/4x-20+2=3/x-5 equation:

-3/4x-20+2=3/x-5

We move all terms to the left:

-3/4x-20+2-(3/x-5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x-5)!=0

x∈R


We add all the numbers together, and all the variables

-3/4x-(3/x-5)-18=0

We get rid of parentheses

-3/4x-3/x+5-18=0

We calculate fractions


(-3x)/4x^2+(-12x)/4x^2+5-18=0

We add all the numbers together, and all the variables

(-3x)/4x^2+(-12x)/4x^2-13=0

We multiply all the terms by the denominator


(-3x)+(-12x)-13*4x^2=0

Wy multiply elements

-52x^2+(-3x)+(-12x)=0

We get rid of parentheses

-52x^2-3x-12x=0

We add all the numbers together, and all the variables

-52x^2-15x=0

a = -52; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-52)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-52}=\frac{0}{-104}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-52}=\frac{30}{-104}
=-15/52
$