X(5x-13)=6

Solution for X(5x-13)=6 equation:

X(5X-13)=6

We move all terms to the left:

X(5X-13)-(6)=0

We multiply parentheses

5X^2-13X-6=0

a = 5; b = -13; c = -6;
Δ = b2-4ac
Δ = -132-4·5·(-6)
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{-(-13)-17}{2*5}=\frac{-4}{10}
=-2/5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+17}{2*5}=\frac{30}{10}
=3
$