2x+16=6/7x

Solution for 2x+16=6/7x equation:

2x+16=6/7x

We move all terms to the left:

2x+16-(6/7x)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+6/7x)+16=0

We get rid of parentheses

2x-6/7x+16=0

We multiply all the terms by the denominator


2x*7x+16*7x-6=0

Wy multiply elements

14x^2+112x-6=0

a = 14; b = 112; c = -6;
Δ = b2-4ac
Δ = 1122-4·14·(-6)
Δ = 12880
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:

$\sqrt{\Delta}=\sqrt{12880}=\sqrt{16*805}=\sqrt{16}*\sqrt{805}=4\sqrt{805}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-4\sqrt{805}}{2*14}=\frac{-112-4\sqrt{805}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+4\sqrt{805}}{2*14}=\frac{-112+4\sqrt{805}}{28}
$