X-9=1/4x+3

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

X-9=1/4X+3

We move all terms to the left:

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


Domain of the equation: 4X+3)!=0

X∈R


We get rid of parentheses

X-1/4X-3-9=0

We multiply all the terms by the denominator


X*4X-3*4X-9*4X-1=0

Wy multiply elements

4X^2-12X-36X-1=0

We add all the numbers together, and all the variables

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}
$