0=14x2-17x-6

Solution for 0=14x2-17x-6 equation:

0=14x^2-17x-6

We move all terms to the left:

0-(14x^2-17x-6)=0

We add all the numbers together, and all the variables

-(14x^2-17x-6)=0

We get rid of parentheses

-14x^2+17x+6=0

a = -14; b = 17; c = +6;
Δ = b2-4ac
Δ = 172-4·(-14)·6
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-25}{2*-14}=\frac{-42}{-28}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+25}{2*-14}=\frac{8}{-28}
=-2/7
$