x^2+0.5x-10^(-10)=0

Solution for x^2+0.5x-10^(-10)=0 equation:

x^2+0.5x-10^(-10)=0

We add all the numbers together, and all the variables

x^2+0.5x-10-1.0E=0

We add all the numbers together, and all the variables

x^2+0.5x-12.718281828459=0

a = 1; b = 0.5; c = -12.718281828459;
Δ = b2-4ac
Δ = 0.52-4·1·(-12.718281828459)
Δ = 51.123127313836
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{-(0.5)-\sqrt{51.123127313836}}{2*1}=\frac{-0.5-\sqrt{51.123127313836}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{51.123127313836}}{2*1}=\frac{-0.5+\sqrt{51.123127313836}}{2}
$