Question

Solve by using the quadratic formula. (If there is no solution, enter NO SOLUTION.)

1/7x^2+1=3/7x
smaller value of x =
larger value of x=

Answer 1

`\frac 17 x^2 + 1 = \frac 37 x\\\\\implies x^2 +7 =3x~~~;[\text{Multiply both sides by 7}]\\\\\implies x^2 -3x +7 =0\\\\\text{Apply quadratic formula}~ x = (-b \pm √(b^2 -4ac))/(2a).\\\\\text{In this case ,}~ a =1, b= -3 , c =7\\\\x = (-(-3) \pm √((-3)^2 - 4(1)(7))/(2(1))\\\\\implies x= (3 \pm √(-19))/(2)\\\\\implies x =\frac{ 3 \pm i√(19)}2\\\\\\\text{Smaller value of x } =\frac{ 3 -i√(19)}2\\\\\text{Larger value of x } =\frac{ 3 +i√(19)}2`