10/6x+x=112

Solution for 10/6x+x=112 equation:

10/6x+x=112

We move all terms to the left:

10/6x+x-(112)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

x+10/6x-112=0

We multiply all the terms by the denominator


x*6x-112*6x+10=0

Wy multiply elements

6x^2-672x+10=0

a = 6; b = -672; c = +10;
Δ = b2-4ac
Δ = -6722-4·6·10
Δ = 451344
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:

$\sqrt{\Delta}=\sqrt{451344}=\sqrt{16*28209}=\sqrt{16}*\sqrt{28209}=4\sqrt{28209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-672)-4\sqrt{28209}}{2*6}=\frac{672-4\sqrt{28209}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-672)+4\sqrt{28209}}{2*6}=\frac{672+4\sqrt{28209}}{12}
$