0=14x^2+5x-9

Solution for 0=14x^2+5x-9 equation:

0=14x^2+5x-9

We move all terms to the left:

0-(14x^2+5x-9)=0

We add all the numbers together, and all the variables

-(14x^2+5x-9)=0

We get rid of parentheses

-14x^2-5x+9=0

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