X+2/5x=21

Solution for X+2/5x=21 equation:

X+2/5X=21

We move all terms to the left:

X+2/5X-(21)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We multiply all the terms by the denominator


X*5X-21*5X+2=0

Wy multiply elements

5X^2-105X+2=0

a = 5; b = -105; c = +2;
Δ = b2-4ac
Δ = -1052-4·5·2
Δ = 10985
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:

$\sqrt{\Delta}=\sqrt{10985}=\sqrt{169*65}=\sqrt{169}*\sqrt{65}=13\sqrt{65}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-13\sqrt{65}}{2*5}=\frac{105-13\sqrt{65}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+13\sqrt{65}}{2*5}=\frac{105+13\sqrt{65}}{10}
$