0=x^2-18x+69

Solution for 0=x^2-18x+69 equation:

0=x^2-18x+69

We move all terms to the left:

0-(x^2-18x+69)=0

We add all the numbers together, and all the variables

-(x^2-18x+69)=0

We get rid of parentheses

-x^2+18x-69=0

We add all the numbers together, and all the variables

-1x^2+18x-69=0

a = -1; b = 18; c = -69;
Δ = b2-4ac
Δ = 182-4·(-1)·(-69)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{3}}{2*-1}=\frac{-18-4\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{3}}{2*-1}=\frac{-18+4\sqrt{3}}{-2}
$