Question 125014
<pre><b>

the difference between two times the square of a number and five times the number is 75. 

Look at the <font color = "red">red</font> words:

the difference between two times the square of <font color = "red">a number</font> and five times <font color = "red">the number</font> is 75. 	

Replace each by <font color = "red">x</font>.

the difference between two times the square of <font color = "red">x</font> and five times <font color = "red">x</font> is 75. 

Look at the <font color = "blue">blue</font> words:

the difference between two times <font color = "blue">the square of x</font> and five times x is 75. 

Replace them by <font color = "blue">x²</font>

the difference between two times <font color = "blue">x²</font> and five times x is 75.

Look at the <font color = "red">red</font> words:

the difference between two times x² and <font color = "red">five times x </font>is 75.

Replace them by <font color = "red">5x</font>

the difference between two times x² and <font color = "red">5x</font> is 75

Look at the <font color = "blue">blue</font> words:

the difference between <font color = "blue">two times x²</font> and 5x is 75.

Replace them by <font color = "blue">2x²</font>

the difference between <font color = "blue">2x²</font> and 5x is 75.

Look at the <font color = "red">red</font> words:

<font color = "red">the difference between 2x² and 5x</font> is 75.

Replace them by the subtraction of the first minus the second,
or <font color = "red">2x² - 5x</font>

<font color = "red">2x² - 5x</font> is 75.

Look at the blue word:

2x² - 5x <font color = "blue">is</font> 75.

Replace it by an equal sign " <font color = "blue">= </font>":

2x² - 5x <font color = "blue">=</font> 75.
</font>
Solve that:

2x² - 5x - 75 = 0

Factoring:

(2x - 15)(x + 5) = 0

2x - 15 = 0 gives solution x = {{{15/2}}}

x + 5 = 0 gives solution x = -5

Edwin</pre>