Add 24 to both sides so that the equation becomes -7x^2 + 23x - 1 = 0.
To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
x = [ -b ± √(b^2 - 4ac) ] / (2a)
x = [ -23 ± √(23^2 - 4(-7)(-1)) ] / ( 2(-7) )
x = [ -23 ± √(529 - (28) ) ] / ( -14 )
x = [ -23 ± √(501) ] / ( -14)
x = [ -23 ± sqrt(501) ] / ( -14 )
x = 23/14 ± -sqrt(501)/14
The answers are 23/14 + sqrt(501)/14 and 23/14 - sqrt(501)/14.
