X+31/12x+10=46

Solution for X+31/12x+10=46 equation:

X+31/12X+10=46

We move all terms to the left:

X+31/12X+10-(46)=0


Domain of the equation: 12X!=0

X!=0/12

X!=0

X∈R


We add all the numbers together, and all the variables

X+31/12X-36=0

We multiply all the terms by the denominator


X*12X-36*12X+31=0

Wy multiply elements

12X^2-432X+31=0

a = 12; b = -432; c = +31;
Δ = b2-4ac
Δ = -4322-4·12·31
Δ = 185136
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:

$\sqrt{\Delta}=\sqrt{185136}=\sqrt{16*11571}=\sqrt{16}*\sqrt{11571}=4\sqrt{11571}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-432)-4\sqrt{11571}}{2*12}=\frac{432-4\sqrt{11571}}{24}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-432)+4\sqrt{11571}}{2*12}=\frac{432+4\sqrt{11571}}{24}
$