11/12x-x+4=0

Solution for 11/12x-x+4=0 equation:

11/12x-x+4=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+11/12x+4=0

We multiply all the terms by the denominator


-1x*12x+4*12x+11=0

Wy multiply elements

-12x^2+48x+11=0

a = -12; b = 48; c = +11;
Δ = b2-4ac
Δ = 482-4·(-12)·11
Δ = 2832
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:

$\sqrt{\Delta}=\sqrt{2832}=\sqrt{16*177}=\sqrt{16}*\sqrt{177}=4\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{177}}{2*-12}=\frac{-48-4\sqrt{177}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{177}}{2*-12}=\frac{-48+4\sqrt{177}}{-24}
$