X+3/5x=192

Solution for X+3/5x=192 equation:

X+3/5X=192

We move all terms to the left:

X+3/5X-(192)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We multiply all the terms by the denominator


X*5X-192*5X+3=0

Wy multiply elements

5X^2-960X+3=0

a = 5; b = -960; c = +3;
Δ = b2-4ac
Δ = -9602-4·5·3
Δ = 921540
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:

$\sqrt{\Delta}=\sqrt{921540}=\sqrt{4*230385}=\sqrt{4}*\sqrt{230385}=2\sqrt{230385}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-960)-2\sqrt{230385}}{2*5}=\frac{960-2\sqrt{230385}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-960)+2\sqrt{230385}}{2*5}=\frac{960+2\sqrt{230385}}{10}
$