Respuesta :

S1NGH

Answer:

2.57 or -0.907

Step-by-step explanation:

→ First state the quadratic formula

[tex]\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]

→ Identify the 'a', 'b' and 'c' variables

[tex]ax^{2} +bx+c[/tex]

[tex]3x^{2} -5x-7[/tex]

a = 3, b = -5 and c = -7

→ Substitute in the values into the quadratic formula

[tex]\frac{5+\sqrt{5^{2}-4*3*-7 } }{2*3}=\frac{5+\sqrt{25+84 } }{6}=\frac{5+\sqrt{109 } }{6}=2.573384418[/tex]

→ Do the same for negative

[tex]\frac{5-\sqrt{5^{2}-4*3*-7 } }{2*3}=\frac{5-\sqrt{25+84 } }{6}=\frac{5-\sqrt{109 } }{6}=-0.9067177515[/tex]

facundo3141592

The two solutions of the quadratic equation are:

  • x = -2.573
  • x = 0.907.

How to solve a quadratic equation?

For a general quadratic equation:

a*x^2 + b*x + c = 0

The solutions are given by:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

In this case we have:

3x^2 + 5x - 7 = 0

Then:

  • a = 3
  • b = 5
  • c = -7.

Replacing that in the formula we get:

[tex]x = \frac{-5 \pm \sqrt{5^2 - 4*3*(-7)} }{2*3}\\\\x = \frac{-5 \pm 10.44 }{6}[/tex]

Then the two solutions are:

  • x = (-5 + 10.44)/6 = 0.907
  • x = (-5 - 10.44)/6 = -2.573

If you want to learn more about quadratic equations, you can read:

https://brainly.com/question/1214333

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