4x(x-1)=33

Solution for 4x(x-1)=33 equation:

4x(x-1)=33

We move all terms to the left:

4x(x-1)-(33)=0

We multiply parentheses

4x^2-4x-33=0

a = 4; b = -4; c = -33;
Δ = b2-4ac
Δ = -42-4·4·(-33)
Δ = 544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{34}}{2*4}=\frac{4-4\sqrt{34}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{34}}{2*4}=\frac{4+4\sqrt{34}}{8}
$