(x-2)(2x+1)=26*2

Solution for (x-2)(2x+1)=26*2 equation:

(x-2)(2x+1)=26*2

We move all terms to the left:

(x-2)(2x+1)-(26*2)=0

We add all the numbers together, and all the variables

(x-2)(2x+1)-52=0

We multiply parentheses ..

(+2x^2+x-4x-2)-52=0

We get rid of parentheses

2x^2+x-4x-2-52=0

We add all the numbers together, and all the variables

2x^2-3x-54=0

a = 2; b = -3; c = -54;
Δ = b2-4ac
Δ = -32-4·2·(-54)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-21}{2*2}=\frac{-18}{4}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21}{2*2}=\frac{24}{4}
=6
$