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

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

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

We move all terms to the left:

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

We multiply parentheses

-3x^2+9x-(-3x+8)-1=0

We get rid of parentheses

-3x^2+9x+3x-8-1=0

We add all the numbers together, and all the variables

-3x^2+12x-9=0

a = -3; b = 12; c = -9;
Δ = b2-4ac
Δ = 122-4·(-3)·(-9)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6}{2*-3}=\frac{-18}{-6}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6}{2*-3}=\frac{-6}{-6}
=1
$