X(4x-17)=-4

Solution for X(4x-17)=-4 equation:

X(4X-17)=-4

We move all terms to the left:

X(4X-17)-(-4)=0

We add all the numbers together, and all the variables

X(4X-17)+4=0

We multiply parentheses

4X^2-17X+4=0

a = 4; b = -17; c = +4;
Δ = b2-4ac
Δ = -172-4·4·4
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-15}{2*4}=\frac{2}{8}
=1/4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+15}{2*4}=\frac{32}{8}
=4
$