22/4x=12x+126

Solution for 22/4x=12x+126 equation:

22/4x=12x+126

We move all terms to the left:

22/4x-(12x+126)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

22/4x-12x-126=0

We multiply all the terms by the denominator


-12x*4x-126*4x+22=0

Wy multiply elements

-48x^2-504x+22=0

a = -48; b = -504; c = +22;
Δ = b2-4ac
Δ = -5042-4·(-48)·22
Δ = 258240
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:

$\sqrt{\Delta}=\sqrt{258240}=\sqrt{64*4035}=\sqrt{64}*\sqrt{4035}=8\sqrt{4035}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-504)-8\sqrt{4035}}{2*-48}=\frac{504-8\sqrt{4035}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-504)+8\sqrt{4035}}{2*-48}=\frac{504+8\sqrt{4035}}{-96}
$