Solve the following quadratic equation `3q^(2) = 2q+ 8 ` using formula method `:`

Answer

`2, - ( 4)/(3)` are the roots of the given quadratic equation.

Explanation

`3q^(2) = 2q+8`
`:. 3q^(2) - 2q-8 = 0 `
Comparing with the standard for `ax^(2) + bx + c = 0 , a = 3, b= -2, c - 8`
`:. b^(2) - 4ac = ( -2)^(2) - 4(3)( -8) = 4 + 96 = 100`
`:. Sqrt( b^(2) - 4ac ) = 10 `
Now, `q = ( -b+- sqrt(b^(2 ) - 4ac))/(2a) = (-(-2a) +- (10))/(2 xx 3) = ( 2+ 10)/(6)`
`:. q = ( 2+ 10)/( 6) ` or `q = ( 2-10)/( 6)`
`:. q = ( 12)/( 6)` or ` q = - ( 8)/(6)`
`:. q = 2 ` or `q = - ( 4)/( 3) `