6. \( 5 t^{2}+3 t-3=0 \) 7. \( t^{2}-4 t+2=0 \) 8. \( 9\left(k^{2}-1\right)=7 k \) 9. \( 3 f-2=-2 f^{2} \) 10. \( t^{2}+t+1=0 \) nswer and more practice on our Intelligent Practice Service

Let's dive into these quadratic equations with a sprinkle of history! Did you know that the quadratic formula, which we often use to solve equations like these, has been utilized since ancient civilizations? The Babylonians were solving quadratic equations as far back as 2000 BCE using geometric methods, long before the algebraic formulas we use today were developed! Now, when it comes to solving these equations, a common mistake is neglecting to consider the discriminant, which is the part under the square root in the quadratic formula. It tells you the nature of the roots: if it's positive, you'll have two distinct real roots; if it's zero, one repeated root; and if negative, no real roots at all! So always check that first before diving into lengthy calculations!