-5x-2=2x^2

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

-5x-2=2x^2

We move all terms to the left:

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

determiningTheFunctionDomain
-2x^2-5x-2=0

a = -2; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·(-2)·(-2)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*-2}=\frac{2}{-4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*-2}=\frac{8}{-4}
=-2
$