X=3/6y-1

Solution for X=3/6y-1 equation:

X=3/6X-1

We move all terms to the left:

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


Domain of the equation: 6X-1)!=0

X∈R


We get rid of parentheses

X-3/6X+1=0

We multiply all the terms by the denominator


X*6X+1*6X-3=0

Wy multiply elements

6X^2+6X-3=0

a = 6; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·6·(-3)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{3}}{2*6}=\frac{-6-6\sqrt{3}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{3}}{2*6}=\frac{-6+6\sqrt{3}}{12}
$