0=6x^2-5x-14

Solution for 0=6x^2-5x-14 equation:

0=6x^2-5x-14

We move all terms to the left:

0-(6x^2-5x-14)=0

We add all the numbers together, and all the variables

-(6x^2-5x-14)=0

We get rid of parentheses

-6x^2+5x+14=0

a = -6; b = 5; c = +14;
Δ = b2-4ac
Δ = 52-4·(-6)·14
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*-6}=\frac{-24}{-12}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*-6}=\frac{14}{-12}
=-1+1/6
$