6.89x^2-0.4x-0.9=0

Solution for 6.89x^2-0.4x-0.9=0 equation:

6.89x^2-0.4x-0.9=0

a = 6.89; b = -0.4; c = -0.9;
Δ = b2-4ac
Δ = -0.42-4·6.89·(-0.9)
Δ = 24.964
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{-(-0.4)-\sqrt{24.964}}{2*6.89}=\frac{0.4-\sqrt{24.964}}{13.78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.4)+\sqrt{24.964}}{2*6.89}=\frac{0.4+\sqrt{24.964}}{13.78}
$