Question

Solve the following equation using quadratic formula:

6x² – 31x = 105

Answer 1

Comparing equation 6x² – 31x = 105 = 0 with ax² + bx + c = 0, we get:

a = 6, b = –31 and c = –105

By formula,

`x = (-b ± sqrt(b^2 - 4ac))/(2a)`

Substituting values we get:

⇒ `x = (-(-31) ± sqrt((-31)^2 - 4 xx 6 xx (-105)))/(2 xx (6))`

= `(31 ± sqrt(961 + 2520))/12`

= `(31 ± sqrt(3481))/12`

= `(31 ± 59)/12`

= `(31 + 59)/12` or `(31 - 59)/12`

= `90/12` or `(-28)/12`

= `15/2` or `(-7)/3`

Hence, `x = {15/2, (-7)/3}`.