Question

In the following exercises, solve:

$5a^2+26a=24$

Short answer

On solving, we get $a=\frac{4}{5},-6$.

Step-by-step solution

Step 1. Given information.

Consider the given question,

$5a^2+26a=24$

Bring all the terms to one side,

$5a^2+26a-24=0$

On factoring,

role="math" localid="1644849645692" $$\begin{gathered} 5a^2+30a-4a-24=0 \\ 5a\left(a+6\right)-4\left(a+6\right)=0 \\ \left(5a-4\right)\left(a+6\right)=0 \end{gathered}$$

Then,

role="math" localid="1644849654425" $$\begin{gathered} 5a-4=0 \\ a=\frac{4}{5} \end{gathered}$$

Also,

role="math" localid="1644849661549" $$\begin{gathered} a+6=0 \\ a=-6 \end{gathered}$$

Step 2. Check the answers.

Substitute $a=\frac{4}{5}$in the original equation,

$$\begin{gathered} 5{\left(\frac{4}{5}\right)}^2+26\left(\frac{4}{5}\right)=24 \\ \frac{16}{5}+\frac{104}{5}=24 \\ \frac{120}{5}=24 \\ 24=24 \end{gathered}$$

This is true.

Substitute $a=-6$in the original equation,

$$\begin{gathered} 5{\left(-6\right)}^2+26\left(-6\right)=24 \\ 180-156=24 \\ 24=24 \end{gathered}$$

This is also true.