x2-1.69x-5.69=0

Solution for x2-1.69x-5.69=0 equation:

x2-1.69x-5.69=0

We add all the numbers together, and all the variables

x^2-1.69x-5.69=0

a = 1; b = -1.69; c = -5.69;
Δ = b2-4ac
Δ = -1.692-4·1·(-5.69)
Δ = 25.6161
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{-(-1.69)-\sqrt{25.6161}}{2*1}=\frac{1.69-\sqrt{25.6161}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.69)+\sqrt{25.6161}}{2*1}=\frac{1.69+\sqrt{25.6161}}{2}
$