Start by doing a subtraction of 6 to both sides so that the equation becomes -2x^2 + 7x + 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 = [ -7 ± √((7)^2 - 4(-2)(1)) ] / ( 2(-2) ) x = [-7 ± √(49 - (-8) ) ] / ( -4 ) x = [-7 ± √(57) ] / ( -4) x = [-7 ± sqrt(57) ] / ( -4 ) x = 7/4 ± -sqrt(57)/4 The answers are 7/4 + sqrt(57)/4 and 7/4 - sqrt(57)/4.
