2x+5/6x=160

Solution for 2x+5/6x=160 equation:

2x+5/6x=160

We move all terms to the left:

2x+5/6x-(160)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


2x*6x-160*6x+5=0

Wy multiply elements

12x^2-960x+5=0

a = 12; b = -960; c = +5;
Δ = b2-4ac
Δ = -9602-4·12·5
Δ = 921360
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:

$\sqrt{\Delta}=\sqrt{921360}=\sqrt{16*57585}=\sqrt{16}*\sqrt{57585}=4\sqrt{57585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-960)-4\sqrt{57585}}{2*12}=\frac{960-4\sqrt{57585}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-960)+4\sqrt{57585}}{2*12}=\frac{960+4\sqrt{57585}}{24}
$