3x*(x-1)=468

Solution for 3x*(x-1)=468 equation:

3x(x-1)=468

We move all terms to the left:

3x(x-1)-(468)=0

We multiply parentheses

3x^2-3x-468=0

a = 3; b = -3; c = -468;
Δ = b2-4ac
Δ = -32-4·3·(-468)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-75}{2*3}=\frac{-72}{6}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+75}{2*3}=\frac{78}{6}
=13
$