-x^2-6x+11/2=0

Solution for -x^2-6x+11/2=0 equation:

-x^2-6x+11/2=0

We add all the numbers together, and all the variables

-1x^2-6x+11/2=0

We multiply all the terms by the denominator


-1x^2*2-6x*2+11=0

Wy multiply elements

-2x^2-12x+11=0

a = -2; b = -12; c = +11;
Δ = b2-4ac
Δ = -122-4·(-2)·11
Δ = 232
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{58}}{2*-2}=\frac{12-2\sqrt{58}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{58}}{2*-2}=\frac{12+2\sqrt{58}}{-4}
$