76/x+2*x=100

Solution for 76/x+2*x=100 equation:

76/x+2x=100

We move all terms to the left:

76/x+2x-(100)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x+76/x-100=0

We multiply all the terms by the denominator


2x*x-100*x+76=0

We add all the numbers together, and all the variables

-100x+2x*x+76=0

Wy multiply elements

2x^2-100x+76=0

a = 2; b = -100; c = +76;
Δ = b2-4ac
Δ = -1002-4·2·76
Δ = 9392
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:

$\sqrt{\Delta}=\sqrt{9392}=\sqrt{16*587}=\sqrt{16}*\sqrt{587}=4\sqrt{587}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{587}}{2*2}=\frac{100-4\sqrt{587}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{587}}{2*2}=\frac{100+4\sqrt{587}}{4}
$