(x-1)(3x-11)=0

Solution for (x-1)(3x-11)=0 equation:

(x-1)(3x-11)=0

We multiply parentheses ..

(+3x^2-11x-3x+11)=0

We get rid of parentheses

3x^2-11x-3x+11=0

We add all the numbers together, and all the variables

3x^2-14x+11=0

a = 3; b = -14; c = +11;
Δ = b2-4ac
Δ = -142-4·3·11
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-8}{2*3}=\frac{6}{6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+8}{2*3}=\frac{22}{6}
=3+2/3
$