To find the solutions to this equation (3x^2)-2x+7=0, 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 = [ --2 ± √((-2)^2 - 4(3)(7)) ] / ( 2(3) )
x = [2 ± √(4 - (84) ) ] / ( 6 )
x = [2 ± √(-80) ] / ( 6)
x = [2 ± 4*sqrt(5)*i ] / ( 6 )
x = 1/3 ± (2*sqrt(5)*i)/3
The answers are 1/3 + 2/3*sqrt(5)*i and 1/3 - 2/3*sqrt(5)*i
