4x(x+3)-3x(3x+9)=11x-16x-15

Solution for 4x(x+3)-3x(3x+9)=11x-16x-15 equation:

4x(x+3)-3x(3x+9)=11x-16x-15

We move all terms to the left:

4x(x+3)-3x(3x+9)-(11x-16x-15)=0

We add all the numbers together, and all the variables

4x(x+3)-3x(3x+9)-(-5x-15)=0

We multiply parentheses

4x^2-9x^2+12x-27x-(-5x-15)=0

We get rid of parentheses

4x^2-9x^2+12x-27x+5x+15=0

We add all the numbers together, and all the variables

-5x^2-10x+15=0

a = -5; b = -10; c = +15;
Δ = b2-4ac
Δ = -102-4·(-5)·15
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-20}{2*-5}=\frac{-10}{-10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20}{2*-5}=\frac{30}{-10}
=-3
$