Respuesta :

The given question is a quadratic equation and we can use several methods to get the solutions to this question. The solution to the equation are 3/4 and -5/6 and the greater of the two solutions is 3/4

Quadratic Equation

Quadratic equation are polynomials with a second degree as it's highest power.

An example of a quadratic equation is

[tex]y = ax^2 + bx + c[/tex]

The given quadratic equation is [tex]24x^2 + 2x = 15[/tex]

Let's rearrange the equation

[tex]24x^2 + 2x = 15\\24x^2 + 2x - 15 = 0[/tex]

This implies that

  • a = 24
  • b = 2
  • c = -15

The equation or formula of quadratic formula is given as

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

We can substitute the values into the equation and solve

[tex]y = \frac{-b +- \sqrt{b^2 - 4ac} }{2a}\\y = \frac{-2 +- \sqrt{2^2 -4 * 24 * (-15)} }{2*24} \\y = \frac{-2+-\sqrt{4+1440} }{48} \\y = \frac{-2+-\sqrt{1444} }{48} \\y = \frac{-2+- 38}{48} \\y = \frac{-2+38}{48} \\y = \frac{3}{4}\\ \\or\\y = \frac{-2-38}{48} \\y = \frac{-40}{48} \\y = -\frac{5}{6}[/tex]

From the calculations above, the solution to the equation are 3/4 and -5/6 and the greater of the two solutions is 3/4

Learn more on quadratic equation here;

https://brainly.com/question/8649555

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