x^2-3x-8^(-14)=0

Solution for x^2-3x-8^(-14)=0 equation:

x^2-3x-8^(-14)=0

We add all the numbers together, and all the variables

x^2-3x-13-2.2737367544323E=0

We add all the numbers together, and all the variables

x^2-3x-19.180657302273=0

a = 1; b = -3; c = -19.180657302273;
Δ = b2-4ac
Δ = -32-4·1·(-19.180657302273)
Δ = 85.722629209092
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{-(-3)-\sqrt{85.722629209092}}{2*1}=\frac{3-\sqrt{85.722629209092}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{85.722629209092}}{2*1}=\frac{3+\sqrt{85.722629209092}}{2}
$