1/2x-24=3x-46

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

1/2x-24=3x-46

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-6x^2+44x+1=0

a = -6; b = 44; c = +1;
Δ = b2-4ac
Δ = 442-4·(-6)·1
Δ = 1960
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:

$\sqrt{\Delta}=\sqrt{1960}=\sqrt{196*10}=\sqrt{196}*\sqrt{10}=14\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-14\sqrt{10}}{2*-6}=\frac{-44-14\sqrt{10}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+14\sqrt{10}}{2*-6}=\frac{-44+14\sqrt{10}}{-12}
$