Quadratic is a type of problem which deals with a variable multiplied by itself- an operation also known as squaring.

Solution:

Let the speed of stream be $x$ km/hr

Given, speed of boat in still water is $8$km/hr.

So, speed of downstream $=\left( 8+x \right)$ km/hr

And, speed of upstream $=\left( 8-x \right)$ km/hr

Using, speed = distance/ time

Time taken by the boat to go $15$ km upstream $=15/\left( 8-x \right)$hr

And, time taken by the boat to return $22$ km downstream $=22/\left( 8+x \right)$hr

From the question, the boat returns to the same point in $5$ hr.

so, $\frac{15}{\left( 8-x \right)}+\frac{22}{\left( 8+x \right)}=5$

$\frac{15\left( 8+x \right)+22\left( 8-x \right)}{\left( 8-x \right)\left( 8+x \right)}=5$

$\frac{120+15x+176-22x}{64+{{x}^{2}}}=5$

$\frac{296-7x}{64-{{x}^{2}}}=5$

$5{{x}^{2}}-7x+296-320=0$

$5{{x}^{2}}-7x-24=0$

$5{{x}^{2}}-15x+8x-24=0$ [by factorisation method]

$5x\left( x-3 \right)+8\left( x-3 \right)=0$

$\left( x-3 \right)\left( 5x+8 \right)=0$

$\therefore $ $x=3,x=-8/5$

As the speed of the stream can never be negative, only the positive solution is considered.

Therefore, the speed of the stream is $3$ km/hr.