# How do you solve 3x^2+27x=108?

Aug 26, 2016

The solutions are the same as the solutions of $3 {x}^{2} + 27 x - 108 = 0$

#### Explanation:

You cam make this equation a bit simpler by dividing it by 3. The solutions don't change. So, the modified equation is:

${x}^{2} + 9 x - 36$

Using the formula for the solutions of $a {x}^{2} + b x + c = 0$, as follows:

${x}_{1 , 2} = \frac{- b \pm \sqrt{{b}^{2} - \left(4 \cdot a \cdot c\right)}}{2 a}$

we have in this case:

${x}_{1 , 2} = \frac{- 9 \pm \sqrt{81 - \left(4 \cdot 1 \cdot \left(- 36\right)\right)}}{2}$, and then we have:

${x}_{1 , 2} = \frac{- 9 \pm \sqrt{81 + 144}}{2} = \frac{- 9 \pm \sqrt{225}}{2} = \frac{- 9 \pm 15}{2}$

Thus, we have the solutions:

${x}_{1} = \frac{- 9 + 15}{2} = \frac{6}{2} = 3$

${x}_{2} = \frac{- 9 - 15}{2} = - \frac{24}{2} = - 12$