3x+4=30/x-5

Solution for 3x+4=30/x-5 equation:

3x+4=30/x-5

We move all terms to the left:

3x+4-(30/x-5)=0


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

x∈R


We get rid of parentheses

3x-30/x+5+4=0

We multiply all the terms by the denominator


3x*x+5*x+4*x-30=0

We add all the numbers together, and all the variables

9x+3x*x-30=0

Wy multiply elements

3x^2+9x-30=0

a = 3; b = 9; c = -30;
Δ = b2-4ac
Δ = 92-4·3·(-30)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-21}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+21}{2*3}=\frac{12}{6}
=2
$