X=-3x^2+5x+9

Solution for X=-3x^2+5x+9 equation:

X=-3X^2+5X+9

We move all terms to the left:

X-(-3X^2+5X+9)=0

We get rid of parentheses

3X^2-5X+X-9=0

We add all the numbers together, and all the variables

3X^2-4X-9=0

a = 3; b = -4; c = -9;
Δ = b2-4ac
Δ = -42-4·3·(-9)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{31}}{2*3}=\frac{4-2\sqrt{31}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{31}}{2*3}=\frac{4+2\sqrt{31}}{6}
$