Chapter 2, Problem 1RE

In Problem 1-10, find the real solutions to each quadratic equation.

$3x^2+10x=5x$

To determine

To calculate: The real solutions of the quadratic equation $3x^2+10x=5x$.

Answer to Problem 1RE

Solution:

The real solutions of the equation are $0\text{and}-\frac{5}{3}$.

Explanation of Solution

Given Information:

The given quadratic equation is $3x^2+10x=5x$.

Formula used:

Zero product property:

The general form of quadratic equation is $a{x}^2+bx+c=0$ where $a,b,c$ are constants and $a\ne 0$.

For real numbers $a\text{and}b$, $ab=0$ if and only if $a=0\text{or}b=0\text{or}\text{both}$.

Calculation:

To solve the quadratic equation, first write it in the general form.

$3x^2+10x-5x=0$

Simplify the above equation.

$3x^2+5x=0$

Take $x$ as common.

$x\left(3x+5\right)=0$

Use the zero product property,

$\begin{array}{c}x=0\text{or}3x+5=0\\ x=0\text{or}3x=-5\\ x=0\text{or}x=-\frac{5}{3}\end{array}$

Hence, the real solutions of the equation are $0\text{and}-\frac{5}{3}$.