Question 107047
lets start with 2x^2 - 5x = 3

we have to bring everything together to one side of the equals sign. we get
2x^2 - 5x -3=0

the coeffiecient of x^2 (2) is our a (a=2)

the coeffiecient of x   (-5) is our b (b=-5)

the constant is -3                     (c=-3)    

the quadratic formula is {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

{{{x=((5 +- sqrt(49))/4 }}}
{{{x=5 +-1.75}}}
x=6.75 or x= 3.25


The next one is 3x^2 - 2x + 1 = 0
here a=3 b= -2 and c=1

{{{x = (-(-2) +- sqrt( (-2)^2-4*3*(1) ))/(2*3) }}}
this one has a negative under the square root sign so there is no solution ( the graph never crosses the x axis)


Next....
2(x-5)^2 = 3

expand this out first

we get
{{{2(x^2-10x+25)=3}}}
{{{2x^2-20x+50-3=0}}}
{{{2x^2-20x+47=0}}}
a=2 b=-20 c=47

{{{x = (-(-20) +- sqrt( (-20)^2-4*2*(47) ))/(2*2) }}}
you simplify from here

Hope these have helped