12-3x(x-15)=9,

Solution for 12-3x(x-15)=9, equation:

12-3x(x-15)=9.

We move all terms to the left:

12-3x(x-15)-(9.)=0

We add all the numbers together, and all the variables

-3x(x-15)+12-9=0

We add all the numbers together, and all the variables

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

We multiply parentheses

-3x^2+45x+3=0

a = -3; b = 45; c = +3;
Δ = b2-4ac
Δ = 452-4·(-3)·3
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*-3}=\frac{-45-3\sqrt{229}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{229}}{2*-3}=\frac{-45+3\sqrt{229}}{-6}
$