-5x-9=-2x^2

Solution for -5x-9=-2x^2 equation:

-5x-9=-2x^2

We move all terms to the left:

-5x-9-(-2x^2)=0

We get rid of parentheses

2x^2-5x-9=0

a = 2; b = -5; c = -9;
Δ = b2-4ac
Δ = -52-4·2·(-9)
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*2}=\frac{5-\sqrt{97}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{97}}{2*2}=\frac{5+\sqrt{97}}{4}
$