Question

Quadratic formula 2x²+9x-4=0

Answer 1

`2x^2+9x-4=0\ \ \ \ /:2\\\\x^2+(9)/(2)x-2=0\\\\x^2+2x\cdot(9)/(4)+((9)/(4))^2-((9)/(4))^2=2\\\\(x+(9)/(4))^2-(81)/(16)=2\\\\(x+(9)/(4))^2=(32)/(16)+(81)/(16)\\\\(x+(9)/(4))^2=(113)/(16)\iff x+(9)/(4)=-\sqrt(113)/(16)\ \vee\ x+(9)/(4)=\sqrt(113)/(16)\\\\x=-(9)/(4)-(√(113))/(4)\ \vee\ x=-(9)/(4)+(√(113))/(4)\\\\x=-(9+√(113))/(4)\ \vee\ x=-(9-√(113))/(4)`

Answer 2

`2x^2+9x-4=0 \\ \\a=2 , b =9 , \ c=- 4 \\ \\\Delta = b^(2)-4ac = 9^(2)-4*2* (- 4)= 81+32 =113 \\ \\x_(1)=(-b-√(\Delta ))/(2a) =(-9- √(113))/(4) \\\\x_(2)=(-b+√(\Delta ))/(2a) = (-9+√(113))/(4)`