3/5x+x=232

Solution for 3/5x+x=232 equation:

3/5x+x=232

We move all terms to the left:

3/5x+x-(232)=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+3/5x-232=0

We multiply all the terms by the denominator


x*5x-232*5x+3=0

Wy multiply elements

5x^2-1160x+3=0

a = 5; b = -1160; c = +3;
Δ = b2-4ac
Δ = -11602-4·5·3
Δ = 1345540
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:

$\sqrt{\Delta}=\sqrt{1345540}=\sqrt{196*6865}=\sqrt{196}*\sqrt{6865}=14\sqrt{6865}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1160)-14\sqrt{6865}}{2*5}=\frac{1160-14\sqrt{6865}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1160)+14\sqrt{6865}}{2*5}=\frac{1160+14\sqrt{6865}}{10}
$