5x-3x(9-x)=4

Solution for 5x-3x(9-x)=4 equation:

5x-3x(9-x)=4

We move all terms to the left:

5x-3x(9-x)-(4)=0

We add all the numbers together, and all the variables

5x-3x(-1x+9)-4=0

We multiply parentheses

3x^2+5x-27x-4=0

We add all the numbers together, and all the variables

3x^2-22x-4=0

a = 3; b = -22; c = -4;
Δ = b2-4ac
Δ = -222-4·3·(-4)
Δ = 532
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:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{133}}{2*3}=\frac{22-2\sqrt{133}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{133}}{2*3}=\frac{22+2\sqrt{133}}{6}
$