X(5x-17)=12

Solution for X(5x-17)=12 equation:

X(5X-17)=12

We move all terms to the left:

X(5X-17)-(12)=0

We multiply parentheses

5X^2-17X-12=0

a = 5; b = -17; c = -12;
Δ = b2-4ac
Δ = -172-4·5·(-12)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-23}{2*5}=\frac{-6}{10}
=-3/5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+23}{2*5}=\frac{40}{10}
=4
$