-0.5x^2+6.5x-1=0

Solution for -0.5x^2+6.5x-1=0 equation:

-0.5x^2+6.5x-1=0

a = -0.5; b = 6.5; c = -1;
Δ = b2-4ac
Δ = 6.52-4·(-0.5)·(-1)
Δ = 40.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6.5)-\sqrt{40.25}}{2*-0.5}=\frac{-6.5-\sqrt{40.25}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6.5)+\sqrt{40.25}}{2*-0.5}=\frac{-6.5+\sqrt{40.25}}{-1}
$