(x-4)(2x+1)=26

Solution for (x-4)(2x+1)=26 equation:

(x-4)(2x+1)=26

We move all terms to the left:

(x-4)(2x+1)-(26)=0

We multiply parentheses ..

(+2x^2+x-8x-4)-26=0

We get rid of parentheses

2x^2+x-8x-4-26=0

We add all the numbers together, and all the variables

2x^2-7x-30=0

a = 2; b = -7; c = -30;
Δ = b2-4ac
Δ = -72-4·2·(-30)
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{-(-7)-17}{2*2}=\frac{-10}{4}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+17}{2*2}=\frac{24}{4}
=6
$