3x-6=1/2x+30

Solution for 3x-6=1/2x+30 equation:

3x-6=1/2x+30

We move all terms to the left:

3x-6-(1/2x+30)=0


Domain of the equation: 2x+30)!=0

x∈R


We get rid of parentheses

3x-1/2x-30-6=0

We multiply all the terms by the denominator


3x*2x-30*2x-6*2x-1=0

Wy multiply elements

6x^2-60x-12x-1=0

We add all the numbers together, and all the variables

6x^2-72x-1=0

a = 6; b = -72; c = -1;
Δ = b2-4ac
Δ = -722-4·6·(-1)
Δ = 5208
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:

$\sqrt{\Delta}=\sqrt{5208}=\sqrt{4*1302}=\sqrt{4}*\sqrt{1302}=2\sqrt{1302}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1302}}{2*6}=\frac{72-2\sqrt{1302}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1302}}{2*6}=\frac{72+2\sqrt{1302}}{12}
$