x+2/5x=288

Solution for x+2/5x=288 equation:

x+2/5x=288

We move all terms to the left:

x+2/5x-(288)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-288*5x+2=0

Wy multiply elements

5x^2-1440x+2=0

a = 5; b = -1440; c = +2;
Δ = b2-4ac
Δ = -14402-4·5·2
Δ = 2073560
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:

$\sqrt{\Delta}=\sqrt{2073560}=\sqrt{4*518390}=\sqrt{4}*\sqrt{518390}=2\sqrt{518390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1440)-2\sqrt{518390}}{2*5}=\frac{1440-2\sqrt{518390}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1440)+2\sqrt{518390}}{2*5}=\frac{1440+2\sqrt{518390}}{10}
$