x^2-18x+83=3

Solution for x^2-18x+83=3 equation:

x^2-18x+83=3

We move all terms to the left:

x^2-18x+83-(3)=0

We add all the numbers together, and all the variables

x^2-18x+80=0

a = 1; b = -18; c = +80;
Δ = b2-4ac
Δ = -182-4·1·80
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2}{2*1}=\frac{16}{2}
=8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2}{2*1}=\frac{20}{2}
=10
$