1/4x+23=x+11

Solution for 1/4x+23=x+11 equation:

1/4x+23=x+11

We move all terms to the left:

1/4x+23-(x+11)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-x-11+23=0

We multiply all the terms by the denominator


-x*4x-11*4x+23*4x+1=0

Wy multiply elements

-4x^2-44x+92x+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}
$