Answer:
[tex]\large\boxed{x=-\dfrac{7-\sqrt{97}}{4}\ \vee\ x=-\dfrac{7+\sqrt{97}}{4}}[/tex]
Step-by-step explanation:
[tex]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=\dfrac{-b}{2a}\\\text{if}\ \Delta>0,\ \text{then an equation has two solutions:}\ x=\dfrac{-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[/tex]
[tex]a=-2,\ b=-7,\ c=6\\\\\Delta=(-7)^2-4(-2)(6)=49+48=97>0\\\\\sqrt\Delta=\sqrt{97}\\\\x=\dfrac{-(-7)\pm\sqrt{97}}{2(-2)}=\dfrac{7\pm\sqrt{97}}{-4}=-\dfrac{7\pm\sqrt{97}}{4}[/tex]
