X(2x-1)-2(x-4)=19

Solution for X(2x-1)-2(x-4)=19 equation:

X(2X-1)-2(X-4)=19

We move all terms to the left:

X(2X-1)-2(X-4)-(19)=0

We multiply parentheses

2X^2-1X-2X+8-19=0

We add all the numbers together, and all the variables

2X^2-3X-11=0

a = 2; b = -3; c = -11;
Δ = b2-4ac
Δ = -32-4·2·(-11)
Δ = 97
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{97}}{2*2}=\frac{3-\sqrt{97}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{97}}{2*2}=\frac{3+\sqrt{97}}{4}
$