x^2-51x+540=1080

Solution for x^2-51x+540=1080 equation:

x^2-51x+540=1080

We move all terms to the left:

x^2-51x+540-(1080)=0

We add all the numbers together, and all the variables

x^2-51x-540=0

a = 1; b = -51; c = -540;
Δ = b2-4ac
Δ = -512-4·1·(-540)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-69}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+69}{2*1}=\frac{120}{2}
=60
$