X^2-19x=83

Solution for X^2-19x=83 equation:

X^2-19X=83

We move all terms to the left:

X^2-19X-(83)=0

a = 1; b = -19; c = -83;
Δ = b2-4ac
Δ = -192-4·1·(-83)
Δ = 693
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{693}=\sqrt{9*77}=\sqrt{9}*\sqrt{77}=3\sqrt{77}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-3\sqrt{77}}{2*1}=\frac{19-3\sqrt{77}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+3\sqrt{77}}{2*1}=\frac{19+3\sqrt{77}}{2}
$