(x)=1/4x-12

Solution for (x)=1/4x-12 equation:

(x)=1/4x-12

We move all terms to the left:

(x)-(1/4x-12)=0


Domain of the equation: 4x-12)!=0

x∈R


We get rid of parentheses

x-1/4x+12=0

We multiply all the terms by the denominator


x*4x+12*4x-1=0

Wy multiply elements

4x^2+48x-1=0

a = 4; b = 48; c = -1;
Δ = b2-4ac
Δ = 482-4·4·(-1)
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{145}}{2*4}=\frac{-48-4\sqrt{145}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{145}}{2*4}=\frac{-48+4\sqrt{145}}{8}
$