X(1-3x)=8x-1

Solution for X(1-3x)=8x-1 equation:

X(1-3X)=8X-1

We move all terms to the left:

X(1-3X)-(8X-1)=0

We add all the numbers together, and all the variables

X(-3X+1)-(8X-1)=0

We multiply parentheses

-3X^2+X-(8X-1)=0

We get rid of parentheses

-3X^2+X-8X+1=0

We add all the numbers together, and all the variables

-3X^2-7X+1=0

a = -3; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·(-3)·1
Δ = 61
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{-(-7)-\sqrt{61}}{2*-3}=\frac{7-\sqrt{61}}{-6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{61}}{2*-3}=\frac{7+\sqrt{61}}{-6}
$