10/6x=x+4

Solution for 10/6x=x+4 equation:

10/6x=x+4

We move all terms to the left:

10/6x-(x+4)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

10/6x-x-4=0

We multiply all the terms by the denominator


-x*6x-4*6x+10=0

Wy multiply elements

-6x^2-24x+10=0

a = -6; b = -24; c = +10;
Δ = b2-4ac
Δ = -242-4·(-6)·10
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{51}}{2*-6}=\frac{24-4\sqrt{51}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{51}}{2*-6}=\frac{24+4\sqrt{51}}{-12}
$