1/48x+12=9x-6

Solution for 1/48x+12=9x-6 equation:

1/48x+12=9x-6

We move all terms to the left:

1/48x+12-(9x-6)=0


Domain of the equation: 48x!=0

x!=0/48

x!=0

x∈R


We get rid of parentheses

1/48x-9x+6+12=0

We multiply all the terms by the denominator


-9x*48x+6*48x+12*48x+1=0

Wy multiply elements

-432x^2+288x+576x+1=0

We add all the numbers together, and all the variables

-432x^2+864x+1=0

a = -432; b = 864; c = +1;
Δ = b2-4ac
Δ = 8642-4·(-432)·1
Δ = 748224
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:

$\sqrt{\Delta}=\sqrt{748224}=\sqrt{576*1299}=\sqrt{576}*\sqrt{1299}=24\sqrt{1299}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(864)-24\sqrt{1299}}{2*-432}=\frac{-864-24\sqrt{1299}}{-864}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(864)+24\sqrt{1299}}{2*-432}=\frac{-864+24\sqrt{1299}}{-864}
$