Q3/x+2x+2x-30=75

Solution for Q3/x+2x+2x-30=75 equation:

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

We move all terms to the left:

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


Domain of the equation: Q!=0

Q∈R


We add all the numbers together, and all the variables

4Q+3/Q-105=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

4Q^2-105Q+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:
$Q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-\sqrt{10977}}{2*4}=\frac{105-\sqrt{10977}}{8}
$
$Q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{10977}}{2*4}=\frac{105+\sqrt{10977}}{8}
$