(2x+1)(x-2)=133

Solution for (2x+1)(x-2)=133 equation:

(2x+1)(x-2)=133

We move all terms to the left:

(2x+1)(x-2)-(133)=0

We multiply parentheses ..

(+2x^2-4x+x-2)-133=0

We get rid of parentheses

2x^2-4x+x-2-133=0

We add all the numbers together, and all the variables

2x^2-3x-135=0

a = 2; b = -3; c = -135;
Δ = b2-4ac
Δ = -32-4·2·(-135)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-33}{2*2}=\frac{-30}{4}
=-7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+33}{2*2}=\frac{36}{4}
=9
$