Question

I need help 5x2+5x-30=0

Answer 1

Hello !

Answer:

`\boxed{\sf x=2\ or\ x=-3}`

Explanation:

`\sf 5x^2+5x-30`

This equation is a quadratic equation in the form ax²+bx+c=0

The solution of this equation is given by the quadratic formula :

`\sf x=(-b\pm √(b^2-4ac))/(2a)`

There are 3 cases depending on the values of the discriminant :

• 
  `b^2-4ac > 0` : 2 real roots
• 
  `b^2-4ac = 0` : no real root
• 
  `b^2-4ac < 0` : no real root

Let's calculate the discriminant :

`\sf b^2-4ac=5^2-4*5*(-30)=625 > 0`

There are 2 real roots.

Now let's use the quadratic formula to find the two roots.

`\sf x=(-5\pm√(5^2-4*5*(-30)))/(2*5)\\x=(-5\pm√(625))/(10) \\x_1=(-5+√(625))/(10)=2\\x_2=(-5-√(625))/(10)=-3\\\boxed{\sf x=2\ or\ x=-3}`

Have a nice day ;)