discriminent of 5x^2+3x=2 solve step by step

To find the discriminant and solve step by
step.

Solution:

The
discriminant of a genaral quadratic equation ax^2+bx+c
is

b^2 - 4ac.

The
given equation  is 5x^2+3x=2 which could be written
as:

5x^2+3x-2 = 0

So a= 5, b=x
and c =-2.

Therefore the discriminant of 5x^2+3x-2 is
3^2-4*4*(-2) = 9+40 = 49.

Solution of the equation 5x^2+3x
=2 , or 5x^2+3x-2 =
0. 

5x^2+3x-2 = 0. Group the
middle term in the left side to facilitate factor the
left.

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

5x(x+1)-2(x+1) =
0

(x+1)(5x-2) = 0

x+1=0, 5x-2
= 0

x = -1  or x = 2/5

An
alternate mwthod of solution:

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

5{[ x^2 + 2(3/(10))+(3/10)^2 ] - (3/10)^2 -2/5 } =
0

5 {(x+3/10)^2 - 49/100} =
0

5{ (x+3/10)^2 - 49/100} = 0. Divide both sides by
5.

(x+3/10)^2 - (7/10)^2 =
0

(x+3/10+7/10)(x+3/10-7/10) = 0, as A^2-B^2=
(A+B)(A-B).

(x+1)(x-4/10) =
0

x +1=0 or x-4/10 = 0

x=-1 or
x=4/10 =2/5.