X(1-3x)=5x-2

Solution for X(1-3x)=5x-2 equation:

X(1-3X)=5X-2

We move all terms to the left:

X(1-3X)-(5X-2)=0

We add all the numbers together, and all the variables

X(-3X+1)-(5X-2)=0

We multiply parentheses

-3X^2+X-(5X-2)=0

We get rid of parentheses

-3X^2+X-5X+2=0

We add all the numbers together, and all the variables

-3X^2-4X+2=0

a = -3; b = -4; c = +2;
Δ = b2-4ac
Δ = -42-4·(-3)·2
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{10}}{2*-3}=\frac{4-2\sqrt{10}}{-6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{10}}{2*-3}=\frac{4+2\sqrt{10}}{-6}
$