0=x^2+10x-169

Solution for 0=x^2+10x-169 equation:

0=x^2+10x-169

We move all terms to the left:

0-(x^2+10x-169)=0

We add all the numbers together, and all the variables

-(x^2+10x-169)=0

We get rid of parentheses

-x^2-10x+169=0

We add all the numbers together, and all the variables

-1x^2-10x+169=0

a = -1; b = -10; c = +169;
Δ = b2-4ac
Δ = -102-4·(-1)·169
Δ = 776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{194}}{2*-1}=\frac{10-2\sqrt{194}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{194}}{2*-1}=\frac{10+2\sqrt{194}}{-2}
$