150+4/6x=x

Solution for 150+4/6x=x equation:

150+4/6x=x

We move all terms to the left:

150+4/6x-(x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+4/6x+150=0

We multiply all the terms by the denominator


-1x*6x+150*6x+4=0

Wy multiply elements

-6x^2+900x+4=0

a = -6; b = 900; c = +4;
Δ = b2-4ac
Δ = 9002-4·(-6)·4
Δ = 810096
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:

$\sqrt{\Delta}=\sqrt{810096}=\sqrt{16*50631}=\sqrt{16}*\sqrt{50631}=4\sqrt{50631}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(900)-4\sqrt{50631}}{2*-6}=\frac{-900-4\sqrt{50631}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(900)+4\sqrt{50631}}{2*-6}=\frac{-900+4\sqrt{50631}}{-12}
$