8/5x+x=52

Solution for 8/5x+x=52 equation:

8/5x+x=52

We move all terms to the left:

8/5x+x-(52)=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+8/5x-52=0

We multiply all the terms by the denominator


x*5x-52*5x+8=0

Wy multiply elements

5x^2-260x+8=0

a = 5; b = -260; c = +8;
Δ = b2-4ac
Δ = -2602-4·5·8
Δ = 67440
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:

$\sqrt{\Delta}=\sqrt{67440}=\sqrt{16*4215}=\sqrt{16}*\sqrt{4215}=4\sqrt{4215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-260)-4\sqrt{4215}}{2*5}=\frac{260-4\sqrt{4215}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-260)+4\sqrt{4215}}{2*5}=\frac{260+4\sqrt{4215}}{10}
$