3x*(6-x)/2=2

Solution for 3x*(6-x)/2=2 equation:

3x(6-x)/2=2

We move all terms to the left:

3x(6-x)/2-(2)=0

We add all the numbers together, and all the variables

3x(-1x+6)/2-2=0

We multiply all the terms by the denominator


3x(-1x+6)-2*2=0

We add all the numbers together, and all the variables

3x(-1x+6)-4=0

We multiply parentheses

-3x^2+18x-4=0

a = -3; b = 18; c = -4;
Δ = b2-4ac
Δ = 182-4·(-3)·(-4)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{69}}{2*-3}=\frac{-18-2\sqrt{69}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{69}}{2*-3}=\frac{-18+2\sqrt{69}}{-6}
$