x^2-21x+57=3

Solution for x^2-21x+57=3 equation:

x^2-21x+57=3

We move all terms to the left:

x^2-21x+57-(3)=0

We add all the numbers together, and all the variables

x^2-21x+54=0

a = 1; b = -21; c = +54;
Δ = b2-4ac
Δ = -212-4·1·54
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-15}{2*1}=\frac{6}{2}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+15}{2*1}=\frac{36}{2}
=18
$