Question

Please help, this will just take a minute of your time ❤︎ (literally)
(Discriminant Worksheet)

Answer 1

`\large\boxed{x=-(7-√(97))/(4)\ \vee\ x=-(7+√(97))/(4)}`

Explanation:

`ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\\text{if}\ \Delta<0,\ \text{then an equation has not solution}\\\text{if}\ \Delta=0,\ \text{then an equation has one solution:}\ x=(-b)/(2a)\\\text{if}\ \Delta>0,\ \text{then an equation has two solutions:}\ x=(-b\pm\sqrt\Delta)/(2a)\\\\\text{We have:}\\\\-2x^2-7x+10=4\qquad\text{subtract 4 from both sides}\\\\-2x^2-7x+6=0`

`a=-2,\ b=-7,\ c=6\\\\\Delta=(-7)^2-4(-2)(6)=49+48=97>0\\\\\sqrt\Delta=√(97)\\\\x=(-(-7)\pm√(97))/(2(-2))=(7\pm√(97))/(-4)=-(7\pm√(97))/(4)`