X(5x-14)=24

Solution for X(5x-14)=24 equation:

X(5X-14)=24

We move all terms to the left:

X(5X-14)-(24)=0

We multiply parentheses

5X^2-14X-24=0

a = 5; b = -14; c = -24;
Δ = b2-4ac
Δ = -142-4·5·(-24)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-26}{2*5}=\frac{-12}{10}
=-1+1/5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+26}{2*5}=\frac{40}{10}
=4
$