How do you solve #-5x^2 + 5x + 60 = 0# using the quadratic formula?

Question

Nathan Axel · Accepted Answer

The solutions are
#color(blue)(x=-3, x=4# #−5x^2+5x+60=0# The equation is of the form #color(blue)(ax^2+bx+c=0# where: #a=-5, b=5, c=60# The Discriminant is given by: #color(blue)(Delta=b^2-4*a*c# # = (5)^2-(4*(-5)*60)# # = 25 + 1200=1225# The solutions are found using the formula: #color(blue)(x=(-b+-sqrtDelta)/(2*a)# #x = ((-5)+-sqrt(1225))/(2*(-5)) = ((-5+-35))/-10# Solution 1: #x=(-5+35)/-10 = 30/(-10)# #color(blue)(x=-3# Solution 2: #x=(-5-35)/-10 = -40/-10# #color(blue)(x=4#

Eli Assouline · Answer

undefined To solve the quadratic equation -5x^2 + 5x + 60 = 0 using the quadratic formula, follow these steps:

1. Identify the coefficients a, b, and c in the equation, where a = -5, b = 5, and c = 60.
2. Substitute the values of a, b, and c into the quadratic formula: 
   x = (-b ± √(b^2 - 4ac)) / (2a)
3. Plug in the values:
   x = (-(5) ± √((5)^2 - 4(-5)(60))) / (2(-5))
4. Simplify inside the square root:
   x = (-(5) ± √(25 + 1200)) / (-10)
   x = (-(5) ± √(1225)) / (-10)
5. Find the square root:
   √1225 = 35
6. Substitute the square root value back into the equation:
   x = (-(5) ± 35) / (-10)
7. Simplify:
   x = (-5 + 35) / (-10) or x = (-5 - 35) / (-10)
   x = 30 / (-10) or x = -40 / (-10)
8. Further simplify:
   x = -3 or x = 4

Therefore, the solutions to the equation -5x^2 + 5x + 60 = 0 are x = -3 and x = 4.