Chapter SH, Problem 9.23EP

To determine

To solve equation by using Quadratic Formula.

Answer to Problem 9.23EP

  $x=1.1,-4.4$

Explanation of Solution

Given information :

The function provided is $3x^2+10x=15$

Formula used :

To solve the equation using quadratic formula we need substitute values in the quadratic form given below. This can be found by using $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . Here ‘ a’ , ‘ b’ and ‘ c’ are the co-efficient of the given equation.

Here, $a=3,b=10\text{ and}c=-15$

Calculation :

The given quadratic equation.

  $3x^2+10x-15=0$

Putting the values in the formula.

  $x=\frac{-(10)\pm \sqrt{{(10)}^2-4\times 3\times (-15)}}{2\times 3}$

Simplifying the expression.

  $x=\frac{-10\pm \sqrt{100+180}}{6}$

Further simplification

  $x=\frac{-10\pm 16.7}{6}$

Removing the square root

  $x=-1.67\pm 2.78$

First square root is

  $x=1.11$

Second square root is

  $x=-4.45$

Therefore, $x=1.1,-4.45$ .