3x(x-2)+5(2-x)=16

Solution for 3x(x-2)+5(2-x)=16 equation:

3x(x-2)+5(2-x)=16

We move all terms to the left:

3x(x-2)+5(2-x)-(16)=0

We add all the numbers together, and all the variables

3x(x-2)+5(-1x+2)-16=0

We multiply parentheses

3x^2-6x-5x+10-16=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 = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{193}}{2*3}=\frac{11-\sqrt{193}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{193}}{2*3}=\frac{11+\sqrt{193}}{6}
$