4+6x=9/7x

Solution for 4+6x=9/7x equation:

4+6x=9/7x

We move all terms to the left:

4+6x-(9/7x)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(+9/7x)+4=0

We get rid of parentheses

6x-9/7x+4=0

We multiply all the terms by the denominator


6x*7x+4*7x-9=0

Wy multiply elements

42x^2+28x-9=0

a = 42; b = 28; c = -9;
Δ = b2-4ac
Δ = 282-4·42·(-9)
Δ = 2296
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:

$\sqrt{\Delta}=\sqrt{2296}=\sqrt{4*574}=\sqrt{4}*\sqrt{574}=2\sqrt{574}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{574}}{2*42}=\frac{-28-2\sqrt{574}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{574}}{2*42}=\frac{-28+2\sqrt{574}}{84}
$