-5x-2=3x^2

Solution for -5x-2=3x^2 equation:

-5x-2=3x^2

We move all terms to the left:

-5x-2-(3x^2)=0

determiningTheFunctionDomain
-3x^2-5x-2=0

a = -3; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·(-3)·(-2)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-1}{2*-3}=\frac{4}{-6}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*-3}=\frac{6}{-6}
=-1
$