3x(x-11)=91

Solution for 3x(x-11)=91 equation:

3x(x-11)=91

We move all terms to the left:

3x(x-11)-(91)=0

We multiply parentheses

3x^2-33x-91=0

a = 3; b = -33; c = -91;
Δ = b2-4ac
Δ = -332-4·3·(-91)
Δ = 2181
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{-(-33)-\sqrt{2181}}{2*3}=\frac{33-\sqrt{2181}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{2181}}{2*3}=\frac{33+\sqrt{2181}}{6}
$