Question

L-

Use the quadratic formula to find both solutions to the quadratic equation
given below.

3x2 - 7x-1 = 0​

Answer 1

x= 2.468374946 or x= -0.135041612

Step-by-step explanation:

Give each number a term

`{3x}^(2) - 7x - 1 = 0 \\ {ax}^(2) + bx + c = 0`

Write out this formula and substitute

`x = \frac{ - b \binom{ + }{ - } \sqrt{ {b}^(2) - 4ac } }{2a} \\ x = \frac{ - ( - 7) \binom{ + }{ - } \sqrt{ {( - 7)}^(2) - 4(3)( - 1)} }{2(3)}`

Expand the brackets

`x = \frac{7 \binom{ + }{ - } √(41 + 12) }{6} \\ x = \frac{7 \binom{ + }{ - } √(61) }{6}`

Solve for each

`x = (7 + √(61) )/(6) \\ x = 2.468374946`

`x = (7 - √(61) )/(6) \\ x = - 0.135041612`