X2-9x-225=0

Solution for X2-9x-225=0 equation:

X2-9X-225=0

We add all the numbers together, and all the variables

X^2-9X-225=0

a = 1; b = -9; c = -225;
Δ = b2-4ac
Δ = -92-4·1·(-225)
Δ = 981
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:

$\sqrt{\Delta}=\sqrt{981}=\sqrt{9*109}=\sqrt{9}*\sqrt{109}=3\sqrt{109}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{109}}{2*1}=\frac{9-3\sqrt{109}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{109}}{2*1}=\frac{9+3\sqrt{109}}{2}
$