x^2-7x-11/2=0

Solution for x^2-7x-11/2=0 equation:

x^2-7x-11/2=0

We multiply all the terms by the denominator


x^2*2-7x*2-11=0

Wy multiply elements

2x^2-14x-11=0

a = 2; b = -14; c = -11;
Δ = b2-4ac
Δ = -142-4·2·(-11)
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{71}}{2*2}=\frac{14-2\sqrt{71}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{71}}{2*2}=\frac{14+2\sqrt{71}}{4}
$