Question

40 points (i know it says 20 pts but i gave 40) ! SHOW WORK PLEASE, I need answers soon!

Use the quadratic formula to solve 2x^2=5x+6. Im sure the answer is -2x-6, but I need someone to help me double check.

Answer 1

`\large\boxed{x=(5-√(73))/(4)\ or\ x=(5+√(73))/(4)}`

Explanation:

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

`\text{We have}\ 2x^2=5x+6.\ \text{Convert to the form of}\ ax^2+bx+c=0:\\\\2x^2=5x+6\qquad\text{subtract}\ 5x\ \text{and}\ 6\ \text{from both sides}\\\\2x^2-5x-6=0\\\\a=2,\ b=-5,\ c=-6\\\\b^2-4ac=(-5)^2-4(2)(-6)=25+48=73>0\\\\x=(-(-5)\pm√(73))/(2(2))=(5\pm√(73))/(4)`