X^2-84x-83=0

Solution for X^2-84x-83=0 equation:

X^2-84X-83=0

a = 1; b = -84; c = -83;
Δ = b2-4ac
Δ = -842-4·1·(-83)
Δ = 7388
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:

$\sqrt{\Delta}=\sqrt{7388}=\sqrt{4*1847}=\sqrt{4}*\sqrt{1847}=2\sqrt{1847}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1847}}{2*1}=\frac{84-2\sqrt{1847}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1847}}{2*1}=\frac{84+2\sqrt{1847}}{2}
$