Question

Solve for a: a(a-3) =100

Answer 1

$a(a-3) =100\\ a^2-3a-100=0\\ \Delta=(-3)^2-4\cdot1\cdot(-100)=9+400=409\\ \sqrt{\Delta}=\sqr{409}\\ a_1=\dfrac{-(-3)-\sqrt{409}}{2\cdot1}=\dfrac{3-\sqrt{409}}{2}\\ a_2=\dfrac{-(-3)+\sqrt{409}}{2\cdot1}=\dfrac{3+\sqrt{409}}{2}$