x+9/5x=28

Solution for x+9/5x=28 equation:

x+9/5x=28

We move all terms to the left:

x+9/5x-(28)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-28*5x+9=0

Wy multiply elements

5x^2-140x+9=0

a = 5; b = -140; c = +9;
Δ = b2-4ac
Δ = -1402-4·5·9
Δ = 19420
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:

$\sqrt{\Delta}=\sqrt{19420}=\sqrt{4*4855}=\sqrt{4}*\sqrt{4855}=2\sqrt{4855}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-2\sqrt{4855}}{2*5}=\frac{140-2\sqrt{4855}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+2\sqrt{4855}}{2*5}=\frac{140+2\sqrt{4855}}{10}
$