X-1/4x=3+9

Solution for X-1/4x=3+9 equation:

X-1/4X=3+9

We move all terms to the left:

X-1/4X-(3+9)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We add all the numbers together, and all the variables

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}
$