Start by adding 34 to both sides so that the equation becomes -7x^2 + 3x + 6 = 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 = [-3 ± √((3)^2 - 4(-7)(6)) ] / ( 2(-7) )
x = [-3 ± √(9 - (-168) ) ] / ( -14 )
x = [-3 ± √(177) ] / ( -14)
x = [-3 ± sqrt(177) ] / ( -14 )
x = 3/14 ± -sqrt(177)/14
The answers are 3/14 + sqrt(177)/14 and 3/14 - sqrt(177)/14.