x2-69x+270=0

Solution for x2-69x+270=0 equation:

x2-69x+270=0

We add all the numbers together, and all the variables

x^2-69x+270=0

a = 1; b = -69; c = +270;
Δ = b2-4ac
Δ = -692-4·1·270
Δ = 3681
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:

$\sqrt{\Delta}=\sqrt{3681}=\sqrt{9*409}=\sqrt{9}*\sqrt{409}=3\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-3\sqrt{409}}{2*1}=\frac{69-3\sqrt{409}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+3\sqrt{409}}{2*1}=\frac{69+3\sqrt{409}}{2}
$