Question

2x squared plus 6 x plus 3 is equal to 0.....

Answer 1

2x^2 + 6x +3 = 0
That does not factor into terms with integers. Use the quadratic formula
x= [-b +/-sqrt(b^2-4ac)]/2a

x = [-6 +/-sqrt(36 -24)]/4
= [-6 +/-sqrt12]/4
= -2.366 or -0.634

Answer 2

2 x ^ 2 + 6 x + 3 = 0

Compare your equation to the standard form :

a x ^ 2 + b x + c = 0

and identify the values for a , b , c.

a = 2

b = 6

c = 3

Now evaluate the discriminant :

b ^ 2 - 4 a c = 6 ^ 2 - 4 * 2 * 3 = 36 -
24 = 12

Since b ^ 2 - 4 ac > 0 there are two unequal real solutions:


x1 = [ - b + sqrt ( b ^ 2 - 4 a c ) ] / 2 a

x1 = [ - 6 + sqrt ( 12 ) ] / 2 * 2

x1 = [ - 6 + sqrt ( 4 * 3 ) ] / 4

x1 = [ - 6 + 2 * sqrt ( 3 ) ] / 4

x1 = 2 * [ - 3 + sqrt ( 3 ) ] / 2 * 2

x1 = [ - 3 + sqrt ( 3 ) ] / 2

x1 = [ sqrt ( 3 ) - 3 ] / 2

x1 = - 0.63 approx.


x2 = [ - b - sqrt ( b ^ 2 - 4 a c ) ] / 2 a

x2 = [ - 6 - sqrt ( 12 ) ] / 2 * 2

x2 = [ - 6 - sqrt ( 4 * 3 ) ] / 4

x2 = [ - 6 - 2 * sqrt ( 3 ) ] / 4

x2 = 2 * [ - 3 - sqrt ( 3 ) ] / 2 * 2

x2 = [ - 3 - sqrt ( 3 ) ] / 2

x2 = [ - 3 - sqrt ( 3 ) ] / 2

x2 = - 2.37 approx.