X+1/3x+6=74

Solution for X+1/3x+6=74 equation:

X+1/3X+6=74

We move all terms to the left:

X+1/3X+6-(74)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X+1/3X-68=0

We multiply all the terms by the denominator


X*3X-68*3X+1=0

Wy multiply elements

3X^2-204X+1=0

a = 3; b = -204; c = +1;
Δ = b2-4ac
Δ = -2042-4·3·1
Δ = 41604
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:

$\sqrt{\Delta}=\sqrt{41604}=\sqrt{4*10401}=\sqrt{4}*\sqrt{10401}=2\sqrt{10401}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-2\sqrt{10401}}{2*3}=\frac{204-2\sqrt{10401}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+2\sqrt{10401}}{2*3}=\frac{204+2\sqrt{10401}}{6}
$