10=3x(x-1)-8

Solution for 10=3x(x-1)-8 equation:

10=3x(x-1)-8

We move all terms to the left:

10-(3x(x-1)-8)=0


We calculate terms in parentheses: -(3x(x-1)-8), so:

3x(x-1)-8

We multiply parentheses

3x^2-3x-8

Back to the equation:

-(3x^2-3x-8)


We get rid of parentheses

-3x^2+3x+8+10=0

We add all the numbers together, and all the variables

-3x^2+3x+18=0

a = -3; b = 3; c = +18;
Δ = b2-4ac
Δ = 32-4·(-3)·18
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-15}{2*-3}=\frac{-18}{-6}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+15}{2*-3}=\frac{12}{-6}
=-2
$