0=7x^2+17x-12

Solution for 0=7x^2+17x-12 equation:

0=7x^2+17x-12

We move all terms to the left:

0-(7x^2+17x-12)=0

We add all the numbers together, and all the variables

-(7x^2+17x-12)=0

We get rid of parentheses

-7x^2-17x+12=0

a = -7; b = -17; c = +12;
Δ = b2-4ac
Δ = -172-4·(-7)·12
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*-7}=\frac{-8}{-14}
=4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+25}{2*-7}=\frac{42}{-14}
=-3
$