How do you solve -24= a ^ { 2} - 12\cdot 12a?

Dec 6, 2017

${a}_{1} = 0.17$
${a}_{2} = 143.83$

Explanation:

if you rewrite this equation to:
${a}^{2} - 144 a + 24 = 0$
then
a=1 (it's the number in fron of the number ${a}^{2}$)
b=-144
c=24
The well known formula:
${x}_{1 | 2} = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

in our case we are finding the $a$ so it should be a bit different (instead of a letter x the should be a) but then it gets a bit confusing. So let's just substitute those number: a,b,c and find its value

${x}_{1 | 2} = \frac{- \left(- 144\right) \pm \sqrt{{\left(- 144\right)}^{2} - 4 \cdot 1 \cdot 24}}{2 \cdot 1}$
with the help of calculator we get this

${x}_{1 | 2} = \frac{144 \pm \sqrt{20736 - 96}}{2}$

${x}_{1 | 2} = \frac{144 \pm \sqrt{20736 - 96}}{2}$

that is approximately

${x}_{1 | 2} \approx \frac{144 \pm \left(143.66\right)}{2}$

When I said that we are looking for $a$ as it stands in the top so don't mind that there is ${x}_{1 | 2} =$ it's the same just written a bit different. so
${a}_{1} \approx \frac{0.34}{2} = 0.17$
${a}_{2} \approx \frac{287.66}{2} = 143.83$