X-2+3/5x=14

Solution for X-2+3/5x=14 equation:

X-2+3/5X=14

We move all terms to the left:

X-2+3/5X-(14)=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-16=0

We multiply all the terms by the denominator


X*5X-16*5X+3=0

Wy multiply elements

5X^2-80X+3=0

a = 5; b = -80; c = +3;
Δ = b2-4ac
Δ = -802-4·5·3
Δ = 6340
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:

$\sqrt{\Delta}=\sqrt{6340}=\sqrt{4*1585}=\sqrt{4}*\sqrt{1585}=2\sqrt{1585}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{1585}}{2*5}=\frac{80-2\sqrt{1585}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{1585}}{2*5}=\frac{80+2\sqrt{1585}}{10}
$