0=5x^2-3x-2

Solution for 0=5x^2-3x-2 equation:

0=5x^2-3x-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -5; b = 3; c = +2;
Δ = b2-4ac
Δ = 32-4·(-5)·2
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-7}{2*-5}=\frac{-10}{-10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+7}{2*-5}=\frac{4}{-10}
=-2/5
$