3x(x-1)=19

Solution for 3x(x-1)=19 equation:

3x(x-1)=19

We move all terms to the left:

3x(x-1)-(19)=0

We multiply parentheses

3x^2-3x-19=0

a = 3; b = -3; c = -19;
Δ = b2-4ac
Δ = -32-4·3·(-19)
Δ = 237
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{-(-3)-\sqrt{237}}{2*3}=\frac{3-\sqrt{237}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{237}}{2*3}=\frac{3+\sqrt{237}}{6}
$