(2x+1)(x-2)=69

Solution for (2x+1)(x-2)=69 equation:

(2x+1)(x-2)=69

We move all terms to the left:

(2x+1)(x-2)-(69)=0

We multiply parentheses ..

(+2x^2-4x+x-2)-69=0

We get rid of parentheses

2x^2-4x+x-2-69=0

We add all the numbers together, and all the variables

2x^2-3x-71=0

a = 2; b = -3; c = -71;
Δ = b2-4ac
Δ = -32-4·2·(-71)
Δ = 577
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{-(-3)-\sqrt{577}}{2*2}=\frac{3-\sqrt{577}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{577}}{2*2}=\frac{3+\sqrt{577}}{4}
$