x^2-83x+1722=0

Solution for x^2-83x+1722=0 equation:

x^2-83x+1722=0

a = 1; b = -83; c = +1722;
Δ = b2-4ac
Δ = -832-4·1·1722
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-83)-1}{2*1}=\frac{82}{2}
=41
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-83)+1}{2*1}=\frac{84}{2}
=42
$