0=x^2-17x+69

Solution for 0=x^2-17x+69 equation:

0=x^2-17x+69

We move all terms to the left:

0-(x^2-17x+69)=0

We add all the numbers together, and all the variables

-(x^2-17x+69)=0

We get rid of parentheses

-x^2+17x-69=0

We add all the numbers together, and all the variables

-1x^2+17x-69=0

a = -1; b = 17; c = -69;
Δ = b2-4ac
Δ = 172-4·(-1)·(-69)
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{13}}{2*-1}=\frac{-17-\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{13}}{2*-1}=\frac{-17+\sqrt{13}}{-2}
$