7x+6=1/2x

Solution for 7x+6=1/2x equation:

7x+6=1/2x

We move all terms to the left:

7x+6-(1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7x-(+1/2x)+6=0

We get rid of parentheses

7x-1/2x+6=0

We multiply all the terms by the denominator


7x*2x+6*2x-1=0

Wy multiply elements

14x^2+12x-1=0

a = 14; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·14·(-1)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-10\sqrt{2}}{2*14}=\frac{-12-10\sqrt{2}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+10\sqrt{2}}{2*14}=\frac{-12+10\sqrt{2}}{28}
$