x(9x-5)-14=0

Solution for x(9x-5)-14=0 equation:

x(9x-5)-14=0

We multiply parentheses

9x^2-5x-14=0

a = 9; b = -5; c = -14;
Δ = b2-4ac
Δ = -52-4·9·(-14)
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{-(-5)-23}{2*9}=\frac{-18}{18}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+23}{2*9}=\frac{28}{18}
=1+5/9
$