Question 762611
Equation is {{{5*x^2 - 2*x - 3 = 0}}}
We can solve it through factorization.

Any equation of the form {{{a*x^2 + b^x + c = 0}}}, if it has two factors f1 and f2, then f1*f2 = a*c, f1+f2 = b

{{{5*x^2 - 5*x + 3*x - 3 = 0}}}

{{{5*x(x - 1) + 3*(x - 1) = 0}}}

{{{(5*x + 3)*(x - 1) = 0}}}

So the roots are:
{{{5*x + 3 = 0}}} or {{{x = -3/5}}}
{{{x - 1 = 0}}} or {{{x = 1}}}

Roots of the equation are {{{highlight(-3/5)}}} and {{{highlight(1)}}}

You can also solve it using the standard quadratic solution formula as described below.

*[invoke quadratic "x", 5, -2, -3 ]