3x=1/2x+30

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

3x=1/2x+30

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

3x-1/2x-30=0

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-60x-1=0

a = 6; b = -60; c = -1;
Δ = b2-4ac
Δ = -602-4·6·(-1)
Δ = 3624
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:

$\sqrt{\Delta}=\sqrt{3624}=\sqrt{4*906}=\sqrt{4}*\sqrt{906}=2\sqrt{906}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{906}}{2*6}=\frac{60-2\sqrt{906}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{906}}{2*6}=\frac{60+2\sqrt{906}}{12}
$