30/x-20/(x-3)+4=0

Solution for 30/x-20/(x-3)+4=0 equation:

30/x-20/(x-3)+4=0


Domain of the equation: x!=0

x∈R



Domain of the equation: (x-3)!=0

We move all terms containing x to the left, all other terms to the right

x!=3

x∈R


We calculate fractions


(30x-90)/(x^2-3x)+(-20x)/(x^2-3x)+4=0

We multiply all the terms by the denominator


(30x-90)+(-20x)+4*(x^2-3x)=0

We multiply parentheses

4x^2+(30x-90)+(-20x)-12x=0

We get rid of parentheses

4x^2+30x-20x-12x-90=0

We add all the numbers together, and all the variables

4x^2-2x-90=0

a = 4; b = -2; c = -90;
Δ = b2-4ac
Δ = -22-4·4·(-90)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-38}{2*4}=\frac{-36}{8}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+38}{2*4}=\frac{40}{8}
=5
$