X^2-102x-216=0

Solution for X^2-102x-216=0 equation:

X^2-102X-216=0

a = 1; b = -102; c = -216;
Δ = b2-4ac
Δ = -1022-4·1·(-216)
Δ = 11268
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:

$\sqrt{\Delta}=\sqrt{11268}=\sqrt{36*313}=\sqrt{36}*\sqrt{313}=6\sqrt{313}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-6\sqrt{313}}{2*1}=\frac{102-6\sqrt{313}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+6\sqrt{313}}{2*1}=\frac{102+6\sqrt{313}}{2}
$