X(6-2y)=3y-1

Solution for X(6-2y)=3y-1 equation:

X(6-2X)=3X-1

We move all terms to the left:

X(6-2X)-(3X-1)=0

We add all the numbers together, and all the variables

X(-2X+6)-(3X-1)=0

We multiply parentheses

-2X^2+6X-(3X-1)=0

We get rid of parentheses

-2X^2+6X-3X+1=0

We add all the numbers together, and all the variables

-2X^2+3X+1=0

a = -2; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-2)·1
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{17}}{2*-2}=\frac{-3-\sqrt{17}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{17}}{2*-2}=\frac{-3+\sqrt{17}}{-4}
$