Question

2) Solve the following quadratic equations a, quadratic formulas ii) 6x² -5x = 8

Answer 1

$S=\mleft\lbrace\frac{5+\sqrt[]{217}}{12},\frac{5-\sqrt[]{217}}{12}\mright\rbrace$

1) We can start solving that, by rewriting it into the standard form:

6x² -5x = 8 Subtract 8 from both sides

6x² -5x -8 = 0

2) Since a≠1 and the coefficients are not divisible by each other, let's use the Quadratic Formula:

Δ =b² - 4ac

Δ =25 -4(6)(-8)

Δ = 25 +192

Δ = 217

$\begin{gathered} x=\frac{-b\pm\sqrt[]{\Delta}}{2a}=\frac{5\pm\sqrt[]{217}}{12}= \\ x_1=\frac{5+\sqrt[]{217}}{12} \\ x_2=\frac{5-\sqrt[]{217}}{12} \end{gathered}$

3) Hence the answers are above, x_1 and x_2 are the roots.