Question

Solve the quadratic equation using the quadratic formula: 3x^2 - 6x = 5

Answer 1

`x_(1) = 1+(2√(6))/(3) \\\\x_(2) = 1-(2√(6))/(3)`

Explanation:

3x^2 - 6x - 5=0

quadratic formula:

`x=\frac{-b+-\sqrt{b^(2)-4*a*c}}{2*a}`

a=3 b=-6 c=-5

`x=\frac{-(-6)+-\sqrt{(-6)^(2)-4*3*-5}}{2*3}`

`x=(6+-√(36+60))/(6) \\\\x=(6+-√(96))/(6) \\\\x=\frac{6+-\sqrt{2^(2)*2^(2)*2*3 }}{6} \\\\x=(6+-4√(6))/(6) \\`

so we have:

`x_(1) = 1+(2√(6))/(3) \\\\x_(2) = 1-(2√(6))/(3)`