5x(x-3)+9=0

Solution for 5x(x-3)+9=0 equation:

5x(x-3)+9=0

We multiply parentheses

5x^2-15x+9=0

a = 5; b = -15; c = +9;
Δ = b2-4ac
Δ = -152-4·5·9
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{5}}{2*5}=\frac{15-3\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{5}}{2*5}=\frac{15+3\sqrt{5}}{10}
$