9x-3x^2/2=12

Solution for 9x-3x^2/2=12 equation:

9x-3x^2/2=12

We move all terms to the left:

9x-3x^2/2-(12)=0

We multiply all the terms by the denominator


-3x^2+9x*2-12*2=0

We add all the numbers together, and all the variables

-3x^2+9x*2-24=0

Wy multiply elements

-3x^2+18x-24=0

a = -3; b = 18; c = -24;
Δ = b2-4ac
Δ = 182-4·(-3)·(-24)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6}{2*-3}=\frac{-24}{-6}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6}{2*-3}=\frac{-12}{-6}
=+2
$