2/5x+x=49

Solution for 2/5x+x=49 equation:

2/5x+x=49

We move all terms to the left:

2/5x+x-(49)=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+2/5x-49=0

We multiply all the terms by the denominator


x*5x-49*5x+2=0

Wy multiply elements

5x^2-245x+2=0

a = 5; b = -245; c = +2;
Δ = b2-4ac
Δ = -2452-4·5·2
Δ = 59985
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:

$\sqrt{\Delta}=\sqrt{59985}=\sqrt{9*6665}=\sqrt{9}*\sqrt{6665}=3\sqrt{6665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-245)-3\sqrt{6665}}{2*5}=\frac{245-3\sqrt{6665}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-245)+3\sqrt{6665}}{2*5}=\frac{245+3\sqrt{6665}}{10}
$