5x(x+9)=-45

Solution for 5x(x+9)=-45 equation:

5x(x+9)=-45

We move all terms to the left:

5x(x+9)-(-45)=0

We add all the numbers together, and all the variables

5x(x+9)+45=0

We multiply parentheses

5x^2+45x+45=0

a = 5; b = 45; c = +45;
Δ = b2-4ac
Δ = 452-4·5·45
Δ = 1125
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:

$\sqrt{\Delta}=\sqrt{1125}=\sqrt{225*5}=\sqrt{225}*\sqrt{5}=15\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-15\sqrt{5}}{2*5}=\frac{-45-15\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+15\sqrt{5}}{2*5}=\frac{-45+15\sqrt{5}}{10}
$