6/5x+x=44

Solution for 6/5x+x=44 equation:

6/5x+x=44

We move all terms to the left:

6/5x+x-(44)=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+6/5x-44=0

We multiply all the terms by the denominator


x*5x-44*5x+6=0

Wy multiply elements

5x^2-220x+6=0

a = 5; b = -220; c = +6;
Δ = b2-4ac
Δ = -2202-4·5·6
Δ = 48280
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:

$\sqrt{\Delta}=\sqrt{48280}=\sqrt{4*12070}=\sqrt{4}*\sqrt{12070}=2\sqrt{12070}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-220)-2\sqrt{12070}}{2*5}=\frac{220-2\sqrt{12070}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-220)+2\sqrt{12070}}{2*5}=\frac{220+2\sqrt{12070}}{10}
$