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

Solution for -6x^2-17x+14=0 equation:

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

a = -6; b = -17; c = +14;
Δ = b2-4ac
Δ = -172-4·(-6)·14
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*-6}=\frac{-8}{-12}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+25}{2*-6}=\frac{42}{-12}
=-3+1/2
$