3/7x=9x+4

Solution for 3/7x=9x+4 equation:

3/7x=9x+4

We move all terms to the left:

3/7x-(9x+4)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

3/7x-9x-4=0

We multiply all the terms by the denominator


-9x*7x-4*7x+3=0

Wy multiply elements

-63x^2-28x+3=0

a = -63; b = -28; c = +3;
Δ = b2-4ac
Δ = -282-4·(-63)·3
Δ = 1540
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:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{385}}{2*-63}=\frac{28-2\sqrt{385}}{-126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{385}}{2*-63}=\frac{28+2\sqrt{385}}{-126}
$