x+3x(5-x)=11

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

x+3x(5-x)=11

We move all terms to the left:

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

We add all the numbers together, and all the variables

x+3x(-1x+5)-11=0

We multiply parentheses

-3x^2+x+15x-11=0

We add all the numbers together, and all the variables

-3x^2+16x-11=0

a = -3; b = 16; c = -11;
Δ = b2-4ac
Δ = 162-4·(-3)·(-11)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{31}}{2*-3}=\frac{-16-2\sqrt{31}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{31}}{2*-3}=\frac{-16+2\sqrt{31}}{-6}
$