3/x+2x+2x-30=75

Solution for 3/x+2x+2x-30=75 equation:

3/x+2x+2x-30=75

We move all terms to the left:

3/x+2x+2x-30-(75)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x+3/x-105=0

We multiply all the terms by the denominator


4x*x-105*x+3=0

We add all the numbers together, and all the variables

-105x+4x*x+3=0

Wy multiply elements

4x^2-105x+3=0

a = 4; b = -105; c = +3;
Δ = b2-4ac
Δ = -1052-4·4·3
Δ = 10977
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{-(-105)-\sqrt{10977}}{2*4}=\frac{105-\sqrt{10977}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{10977}}{2*4}=\frac{105+\sqrt{10977}}{8}
$