2x^2+x^-1+5x=-0,4

Solution for 2x^2+x^-1+5x=-0,4 equation:

2x^2+x^-1+5x=-0.4

We move all terms to the left:

2x^2+x^-1+5x-(-0.4)=0

We add all the numbers together, and all the variables

2x^2+6x-0.6=0

a = 2; b = 6; c = -0.6;
Δ = b2-4ac
Δ = 62-4·2·(-0.6)
Δ = 40.8
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)-\sqrt{40.8}}{2*2}=\frac{-6-\sqrt{40.8}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+\sqrt{40.8}}{2*2}=\frac{-6+\sqrt{40.8}}{4}
$