3x-30=1/2x+120

Solution for 3x-30=1/2x+120 equation:

3x-30=1/2x+120

We move all terms to the left:

3x-30-(1/2x+120)=0


Domain of the equation: 2x+120)!=0

x∈R


We get rid of parentheses

3x-1/2x-120-30=0

We multiply all the terms by the denominator


3x*2x-120*2x-30*2x-1=0

Wy multiply elements

6x^2-240x-60x-1=0

We add all the numbers together, and all the variables

6x^2-300x-1=0

a = 6; b = -300; c = -1;
Δ = b2-4ac
Δ = -3002-4·6·(-1)
Δ = 90024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{90024}=\sqrt{484*186}=\sqrt{484}*\sqrt{186}=22\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-22\sqrt{186}}{2*6}=\frac{300-22\sqrt{186}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+22\sqrt{186}}{2*6}=\frac{300+22\sqrt{186}}{12}
$