2(x-4)(272/x)-4=312

Solution for 2(x-4)(272/x)-4=312 equation:

2(x-4)(272/x)-4=312

We move all terms to the left:

2(x-4)(272/x)-4-(312)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2(x-4)(+272/x)-4-312=0

We add all the numbers together, and all the variables

2(x-4)(+272/x)-316=0

We multiply parentheses ..

2(+272x^2-1088x)-316=0

We multiply parentheses

544x^2-2176x-316=0

a = 544; b = -2176; c = -316;
Δ = b2-4ac
Δ = -21762-4·544·(-316)
Δ = 5422592
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:

$\sqrt{\Delta}=\sqrt{5422592}=\sqrt{256*21182}=\sqrt{256}*\sqrt{21182}=16\sqrt{21182}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2176)-16\sqrt{21182}}{2*544}=\frac{2176-16\sqrt{21182}}{1088}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2176)+16\sqrt{21182}}{2*544}=\frac{2176+16\sqrt{21182}}{1088}
$