9x(5-3x)=11

Solution for 9x(5-3x)=11 equation:

9x(5-3x)=11

We move all terms to the left:

9x(5-3x)-(11)=0

We add all the numbers together, and all the variables

9x(-3x+5)-11=0

We multiply parentheses

-27x^2+45x-11=0

a = -27; b = 45; c = -11;
Δ = b2-4ac
Δ = 452-4·(-27)·(-11)
Δ = 837
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:

$\sqrt{\Delta}=\sqrt{837}=\sqrt{9*93}=\sqrt{9}*\sqrt{93}=3\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{93}}{2*-27}=\frac{-45-3\sqrt{93}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{93}}{2*-27}=\frac{-45+3\sqrt{93}}{-54}
$