7/12x+15=x

Solution for 7/12x+15=x equation:

7/12x+15=x

We move all terms to the left:

7/12x+15-(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+15=0

We multiply all the terms by the denominator


-1x*12x+15*12x+7=0

Wy multiply elements

-12x^2+180x+7=0

a = -12; b = 180; c = +7;
Δ = b2-4ac
Δ = 1802-4·(-12)·7
Δ = 32736
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:

$\sqrt{\Delta}=\sqrt{32736}=\sqrt{16*2046}=\sqrt{16}*\sqrt{2046}=4\sqrt{2046}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-4\sqrt{2046}}{2*-12}=\frac{-180-4\sqrt{2046}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+4\sqrt{2046}}{2*-12}=\frac{-180+4\sqrt{2046}}{-24}
$