2x+4650/x=9500

Solution for 2x+4650/x=9500 equation:

2x+4650/x=9500

We move all terms to the left:

2x+4650/x-(9500)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-9500*x+4650=0

We add all the numbers together, and all the variables

-9500x+2x*x+4650=0

Wy multiply elements

2x^2-9500x+4650=0

a = 2; b = -9500; c = +4650;
Δ = b2-4ac
Δ = -95002-4·2·4650
Δ = 90212800
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:

$\sqrt{\Delta}=\sqrt{90212800}=\sqrt{1600*56383}=\sqrt{1600}*\sqrt{56383}=40\sqrt{56383}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9500)-40\sqrt{56383}}{2*2}=\frac{9500-40\sqrt{56383}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9500)+40\sqrt{56383}}{2*2}=\frac{9500+40\sqrt{56383}}{4}
$