15x(2x-9)+3x=0

Solution for 15x(2x-9)+3x=0 equation:

15x(2x-9)+3x=0

We add all the numbers together, and all the variables

3x+15x(2x-9)=0

We multiply parentheses

30x^2+3x-135x=0

We add all the numbers together, and all the variables

30x^2-132x=0

a = 30; b = -132; c = 0;
Δ = b2-4ac
Δ = -1322-4·30·0
Δ = 17424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17424}=132$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-132}{2*30}=\frac{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+132}{2*30}=\frac{264}{60}
=4+2/5
$