1x-9=1/4x+3

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

1x-9=1/4x+3

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

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}
$