(2x+1)(x-2)=33

Solution for (2x+1)(x-2)=33 equation:

(2x+1)(x-2)=33

We move all terms to the left:

(2x+1)(x-2)-(33)=0

We multiply parentheses ..

(+2x^2-4x+x-2)-33=0

We get rid of parentheses

2x^2-4x+x-2-33=0

We add all the numbers together, and all the variables

2x^2-3x-35=0

a = 2; b = -3; c = -35;
Δ = b2-4ac
Δ = -32-4·2·(-35)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-17}{2*2}=\frac{-14}{4}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+17}{2*2}=\frac{20}{4}
=5
$