6/2x=7x-9

Solution for 6/2x=7x-9 equation:

6/2x=7x-9

We move all terms to the left:

6/2x-(7x-9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

6/2x-7x+9=0

We multiply all the terms by the denominator


-7x*2x+9*2x+6=0

Wy multiply elements

-14x^2+18x+6=0

a = -14; b = 18; c = +6;
Δ = b2-4ac
Δ = 182-4·(-14)·6
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{165}}{2*-14}=\frac{-18-2\sqrt{165}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{165}}{2*-14}=\frac{-18+2\sqrt{165}}{-28}
$