Question 108812
{{{2x^2 -5x = 3}}}

In the standard form {{{ax^2 +bx +c = 0}}}, your equation is:

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

=> you have coefficients:
=> {{{a = 2}}}
=> {{{b = -5}}}
=> {{{c = -3}}}

Then roots are:

{{{x[1,2] =(-b +- sqrt (b^2 -4*a*c )) / (2*a)}}}

{{{x[1,2] =(-(-5) +- sqrt ((-5)^2 -4*2*(-3) )) / (2*2)}}}

{{{x[1,2] =(5 +- sqrt (25 + 24)) / 4}}}

{{{x[1,2] =(5 +- sqrt (49)) / 4}}}……………..{{{sqrt(49) = 7}}}

{{{x[1,2] =(5 +- 7) / 4}}}


{{{x[1] =(5 + 7) / 4}}}

{{{x[1] =12 / 4}}}

{{{x[1] = 3}}}


{{{x[2] =(5 - 7) / 4}}}

{{{x[2] = - 2 / 4}}}

{{{x[2] = - 1 / 2}}}