-3x2-6x+4=-2x2+5x+9

Solution for -3x2-6x+4=-2x2+5x+9 equation:

-3x^2-6x+4=-2x^2+5x+9

We move all terms to the left:

-3x^2-6x+4-(-2x^2+5x+9)=0

We get rid of parentheses

-3x^2+2x^2-5x-6x-9+4=0

We add all the numbers together, and all the variables

-1x^2-11x-5=0

a = -1; b = -11; c = -5;
Δ = b2-4ac
Δ = -112-4·(-1)·(-5)
Δ = 101
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{101}}{2*-1}=\frac{11-\sqrt{101}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{101}}{2*-1}=\frac{11+\sqrt{101}}{-2}
$