Question

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

3x2 - 7x-1 = 0​

Answer 1

Answer:

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

$x = \frac{7 \binom{ + }{ - } \sqrt{41 + 12} }{6} \\ x = \frac{7 \binom{ + }{ - } \sqrt{61} }{6}$

Solve for each

$x = \frac{7 + \sqrt{61} }{6} \\ x = 2.468374946$

$x = \frac{7 - \sqrt{61} }{6} \\ x = - 0.135041612$