3x(40-2x)=9

Solution for 3x(40-2x)=9 equation:

3x(40-2x)=9

We move all terms to the left:

3x(40-2x)-(9)=0

We add all the numbers together, and all the variables

3x(-2x+40)-9=0

We multiply parentheses

-6x^2+120x-9=0

a = -6; b = 120; c = -9;
Δ = b2-4ac
Δ = 1202-4·(-6)·(-9)
Δ = 14184
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:

$\sqrt{\Delta}=\sqrt{14184}=\sqrt{36*394}=\sqrt{36}*\sqrt{394}=6\sqrt{394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-6\sqrt{394}}{2*-6}=\frac{-120-6\sqrt{394}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+6\sqrt{394}}{2*-6}=\frac{-120+6\sqrt{394}}{-12}
$