X+11/12x=54

Solution for X+11/12x=54 equation:

X+11/12X=54

We move all terms to the left:

X+11/12X-(54)=0


Domain of the equation: 12X!=0

X!=0/12

X!=0

X∈R


We multiply all the terms by the denominator


X*12X-54*12X+11=0

Wy multiply elements

12X^2-648X+11=0

a = 12; b = -648; c = +11;
Δ = b2-4ac
Δ = -6482-4·12·11
Δ = 419376
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:

$\sqrt{\Delta}=\sqrt{419376}=\sqrt{16*26211}=\sqrt{16}*\sqrt{26211}=4\sqrt{26211}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-648)-4\sqrt{26211}}{2*12}=\frac{648-4\sqrt{26211}}{24}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-648)+4\sqrt{26211}}{2*12}=\frac{648+4\sqrt{26211}}{24}
$