-14x^2-17x=-6

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

-14x^2-17x=-6

We move all terms to the left:

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

We add all the numbers together, and all the variables

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