4/5x+x=1728

Solution for 4/5x+x=1728 equation:

4/5x+x=1728

We move all terms to the left:

4/5x+x-(1728)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x+4/5x-1728=0

We multiply all the terms by the denominator


x*5x-1728*5x+4=0

Wy multiply elements

5x^2-8640x+4=0

a = 5; b = -8640; c = +4;
Δ = b2-4ac
Δ = -86402-4·5·4
Δ = 74649520
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:

$\sqrt{\Delta}=\sqrt{74649520}=\sqrt{16*4665595}=\sqrt{16}*\sqrt{4665595}=4\sqrt{4665595}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8640)-4\sqrt{4665595}}{2*5}=\frac{8640-4\sqrt{4665595}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8640)+4\sqrt{4665595}}{2*5}=\frac{8640+4\sqrt{4665595}}{10}
$