3x-46=1/2x+24

Solution for 3x-46=1/2x+24 equation:

3x-46=1/2x+24

We move all terms to the left:

3x-46-(1/2x+24)=0


Domain of the equation: 2x+24)!=0

x∈R


We get rid of parentheses

3x-1/2x-24-46=0

We multiply all the terms by the denominator


3x*2x-24*2x-46*2x-1=0

Wy multiply elements

6x^2-48x-92x-1=0

We add all the numbers together, and all the variables

6x^2-140x-1=0

a = 6; b = -140; c = -1;
Δ = b2-4ac
Δ = -1402-4·6·(-1)
Δ = 19624
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:

$\sqrt{\Delta}=\sqrt{19624}=\sqrt{4*4906}=\sqrt{4}*\sqrt{4906}=2\sqrt{4906}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-2\sqrt{4906}}{2*6}=\frac{140-2\sqrt{4906}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+2\sqrt{4906}}{2*6}=\frac{140+2\sqrt{4906}}{12}
$