x^2+45x-9=0

Solution for x^2+45x-9=0 equation:

x^2+45x-9=0

a = 1; b = 45; c = -9;
Δ = b2-4ac
Δ = 452-4·1·(-9)
Δ = 2061
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:

$\sqrt{\Delta}=\sqrt{2061}=\sqrt{9*229}=\sqrt{9}*\sqrt{229}=3\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{229}}{2*1}=\frac{-45-3\sqrt{229}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{229}}{2*1}=\frac{-45+3\sqrt{229}}{2}
$