0=17x^2+2x-15

Solution for 0=17x^2+2x-15 equation:

0=17x^2+2x-15

We move all terms to the left:

0-(17x^2+2x-15)=0

We add all the numbers together, and all the variables

-(17x^2+2x-15)=0

We get rid of parentheses

-17x^2-2x+15=0

a = -17; b = -2; c = +15;
Δ = b2-4ac
Δ = -22-4·(-17)·15
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-32}{2*-17}=\frac{-30}{-34}
=15/17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+32}{2*-17}=\frac{34}{-34}
=-1
$