0,4x^2+30=400/x+2

Solution for 0,4x^2+30=400/x+2 equation:

0.4x^2+30=400/x+2

We move all terms to the left:

0.4x^2+30-(400/x+2)=0


Domain of the equation: x+2)!=0

x∈R


We get rid of parentheses

0.4x^2-400/x-2+30=0

We multiply all the terms by the denominator


(0.4x^2)*x-2*x+30*x-400=0

We add all the numbers together, and all the variables

28x+(0.4x^2)*x-400=0

We multiply parentheses

0x^2+28x-400=0

We add all the numbers together, and all the variables

x^2+28x-400=0

a = 1; b = 28; c = -400;
Δ = b2-4ac
Δ = 282-4·1·(-400)
Δ = 2384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2384}=\sqrt{16*149}=\sqrt{16}*\sqrt{149}=4\sqrt{149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{149}}{2*1}=\frac{-28-4\sqrt{149}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{149}}{2*1}=\frac{-28+4\sqrt{149}}{2}
$