1/2x-24+3x-46=180

Solution for 1/2x-24+3x-46=180 equation:

1/2x-24+3x-46=180

We move all terms to the left:

1/2x-24+3x-46-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/2x-250=0

We multiply all the terms by the denominator


3x*2x-250*2x+1=0

Wy multiply elements

6x^2-500x+1=0

a = 6; b = -500; c = +1;
Δ = b2-4ac
Δ = -5002-4·6·1
Δ = 249976
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:

$\sqrt{\Delta}=\sqrt{249976}=\sqrt{4*62494}=\sqrt{4}*\sqrt{62494}=2\sqrt{62494}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-2\sqrt{62494}}{2*6}=\frac{500-2\sqrt{62494}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+2\sqrt{62494}}{2*6}=\frac{500+2\sqrt{62494}}{12}
$