5x-3x(x+4)=-5+4x+11

Solution for 5x-3x(x+4)=-5+4x+11 equation:

5x-3x(x+4)=-5+4x+11

We move all terms to the left:

5x-3x(x+4)-(-5+4x+11)=0

We add all the numbers together, and all the variables

5x-3x(x+4)-(4x+6)=0

We multiply parentheses

-3x^2+5x-12x-(4x+6)=0

We get rid of parentheses

-3x^2+5x-12x-4x-6=0

We add all the numbers together, and all the variables

-3x^2-11x-6=0

a = -3; b = -11; c = -6;
Δ = b2-4ac
Δ = -112-4·(-3)·(-6)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-7}{2*-3}=\frac{4}{-6}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+7}{2*-3}=\frac{18}{-6}
=-3
$