How many real number solutions does the equation have 0=5x^2+2x-12
a one solution
b two solutions
c infinitely many solutions
d no solutions

A.  two solutions

Step-by-step explanation:

To find the number of real solutions the equation is having, we need to solve first;

0=5x²+2x-12

This equation can be re-written as;

5x²+2x-12 = 0

We will use the formula method to solve

Using formula method;

x = -b ±√b² -  4ac  / 2a

From the equation given,

a = 5   b =  2   and c=-12

x = -2 ± √2² - 4(5)(-12)  /  2(5)

x = -2 ± √4 + 240  /  10

x = -2/10   ± √244 /10

x = ±  1.56

x = - 0.2  ±  1.56

Either    x = -0.2 + 1.56     or     x = -0.2 - 1.56

Either     x  = 1.36                or     x = -1.76

Therfore, this equation have two real number solutions

2(2x + 3) = -4 + 2(2x + 5)

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 6

4x - 6 + 6 = 4x - 6 + 6

4x = 4x

x = x

unlimited solutions.