3x(x+2)+5x(2-x)=-32

Solution for 3x(x+2)+5x(2-x)=-32 equation:

3x(x+2)+5x(2-x)=-32

We move all terms to the left:

3x(x+2)+5x(2-x)-(-32)=0

We add all the numbers together, and all the variables

3x(x+2)+5x(-1x+2)-(-32)=0

We add all the numbers together, and all the variables

3x(x+2)+5x(-1x+2)+32=0

We multiply parentheses

3x^2-5x^2+6x+10x+32=0

We add all the numbers together, and all the variables

-2x^2+16x+32=0

a = -2; b = 16; c = +32;
Δ = b2-4ac
Δ = 162-4·(-2)·32
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16\sqrt{2}}{2*-2}=\frac{-16-16\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16\sqrt{2}}{2*-2}=\frac{-16+16\sqrt{2}}{-4}
$