x*x-69x+1080=0

Solution for x*x-69x+1080=0 equation:

x*x-69x+1080=0

We add all the numbers together, and all the variables

-69x+x*x+1080=0

Wy multiply elements

x^2-69x+1080=0

a = 1; b = -69; c = +1080;
Δ = b2-4ac
Δ = -692-4·1·1080
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-21}{2*1}=\frac{48}{2}
=24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+21}{2*1}=\frac{90}{2}
=45
$