3x(2-x)+8=2+x

Solution for 3x(2-x)+8=2+x equation:

3x(2-x)+8=2+x

We move all terms to the left:

3x(2-x)+8-(2+x)=0

We add all the numbers together, and all the variables

3x(-1x+2)-(x+2)+8=0

We multiply parentheses

-3x^2+6x-(x+2)+8=0

We get rid of parentheses

-3x^2+6x-x-2+8=0

We add all the numbers together, and all the variables

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

a = -3; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·(-3)·6
Δ = 97
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{-(5)-\sqrt{97}}{2*-3}=\frac{-5-\sqrt{97}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{97}}{2*-3}=\frac{-5+\sqrt{97}}{-6}
$