6/10x+x=192

Solution for 6/10x+x=192 equation:

6/10x+x=192

We move all terms to the left:

6/10x+x-(192)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

x+6/10x-192=0

We multiply all the terms by the denominator


x*10x-192*10x+6=0

Wy multiply elements

10x^2-1920x+6=0

a = 10; b = -1920; c = +6;
Δ = b2-4ac
Δ = -19202-4·10·6
Δ = 3686160
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:

$\sqrt{\Delta}=\sqrt{3686160}=\sqrt{16*230385}=\sqrt{16}*\sqrt{230385}=4\sqrt{230385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1920)-4\sqrt{230385}}{2*10}=\frac{1920-4\sqrt{230385}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1920)+4\sqrt{230385}}{2*10}=\frac{1920+4\sqrt{230385}}{20}
$