[tex]\sf x^2 - 3x - 8 = 4 [/tex]
[tex]\longrightarrow \sf x^2 - 3x - 8 - 4 = 0 [/tex]
[tex]\longrightarrow \sf x^2 - 3x - {\red{12}} = 0 [/tex]
You had written (-4) instead of (-12)
[tex]\sf{\\}[/tex]
Quadratic formula:-
[tex]\boxed{\sf{Roots = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}}[/tex]
[tex]\sf{\\}[/tex]
Here,
[tex]\sf{\\}[/tex]
By using quadratic formula,
[tex]\sf{ x_1 = \dfrac{-(-3) + \sqrt{(-3)^2 - 4(1)(-12)}}{2(1)}}[/tex]
[tex]\leadsto \underline{\boxed{\mathfrak{ \pink{x_1 = \dfrac{3 + \sqrt{57}}{2}}}}}[/tex]
Similarly,
[tex]\sf x_2 = \dfrac{-(-3) - \sqrt{(-3)^2 - 4(1)(-12)}}{2(1)}[/tex]
[tex]\leadsto \underline{\boxed{\mathfrak{\pink{ x_2 = \dfrac{3 - \sqrt{57}}{2}}}}}[/tex]
