X-1/6y=4

Solution for X-1/6y=4 equation:

X-1/6X=4

We move all terms to the left:

X-1/6X-(4)=0


Domain of the equation: 6X!=0

X!=0/6

X!=0

X∈R


We multiply all the terms by the denominator


X*6X-4*6X-1=0

Wy multiply elements

6X^2-24X-1=0

a = 6; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·6·(-1)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-10\sqrt{6}}{2*6}=\frac{24-10\sqrt{6}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+10\sqrt{6}}{2*6}=\frac{24+10\sqrt{6}}{12}
$