x+9/5x=112

Solution for x+9/5x=112 equation:

x+9/5x=112

We move all terms to the left:

x+9/5x-(112)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-112*5x+9=0

Wy multiply elements

5x^2-560x+9=0

a = 5; b = -560; c = +9;
Δ = b2-4ac
Δ = -5602-4·5·9
Δ = 313420
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:

$\sqrt{\Delta}=\sqrt{313420}=\sqrt{4*78355}=\sqrt{4}*\sqrt{78355}=2\sqrt{78355}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-560)-2\sqrt{78355}}{2*5}=\frac{560-2\sqrt{78355}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-560)+2\sqrt{78355}}{2*5}=\frac{560+2\sqrt{78355}}{10}
$