7/12x+35=x

Solution for 7/12x+35=x equation:

7/12x+35=x

We move all terms to the left:

7/12x+35-(x)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+7/12x+35=0

We multiply all the terms by the denominator


-1x*12x+35*12x+7=0

Wy multiply elements

-12x^2+420x+7=0

a = -12; b = 420; c = +7;
Δ = b2-4ac
Δ = 4202-4·(-12)·7
Δ = 176736
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:

$\sqrt{\Delta}=\sqrt{176736}=\sqrt{16*11046}=\sqrt{16}*\sqrt{11046}=4\sqrt{11046}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(420)-4\sqrt{11046}}{2*-12}=\frac{-420-4\sqrt{11046}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(420)+4\sqrt{11046}}{2*-12}=\frac{-420+4\sqrt{11046}}{-24}
$