Question

Use the quadratic formula to si
3x2 + 8x – 4= 0

Answer 1

`\large\boxed{x=(-4-2\sqrt7)/(3)\ or\ x=(-4+2\sqrt7)/(3)}`

Explanation:

`\text{The quadratic formula for a quadratic equation}\ ax^2+bx+c=0\\\\\text{determinant:}\ \Delta=b^2-4ac\\\\\text{If}\ \Delta<0,\ \text{then the equation has no solution.}\\\\\text{If}\ \Delta=0,\ \text{then the equation has one solution}\ x=(-b)/(2a).\\\\\text{If}\ \Delta>0,\ \text{then the equation has two different solutions}\ x=(-b\pm\sqrt\Delta)/(2a).`

`\text{We have:}\\\\3x^2+8x-4=0\\\\a=3,\ b=8,\ c=-4\\\\\Delta=8^2-4(3)(-4)=64+48=112>0\\\sqrt\Delta=√(112)=√((16)(7))=√(16)\cdot\sqrt7=4\sqrt7\\\\x=(-8\pm4\sqrt7)/(2(3))=(-8\pm4\sqrt7)/(6)=(2(-4\pm2\sqrt7))/(6)=(-4\pm2\sqrt7)/(3)`