0=6x^2-17x-28

Solution for 0=6x^2-17x-28 equation:

0=6x^2-17x-28

We move all terms to the left:

0-(6x^2-17x-28)=0

We add all the numbers together, and all the variables

-(6x^2-17x-28)=0

We get rid of parentheses

-6x^2+17x+28=0

a = -6; b = 17; c = +28;
Δ = b2-4ac
Δ = 172-4·(-6)·28
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-31}{2*-6}=\frac{-48}{-12}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+31}{2*-6}=\frac{14}{-12}
=-1+1/6
$