.25x+2/3x+50=x

Solution for .25x+2/3x+50=x equation:

.25x+2/3x+50=x

We move all terms to the left:

.25x+2/3x+50-(x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-0.75x+2/3x+50=0

We multiply all the terms by the denominator


-(0.75x)*3x+50*3x+2=0

We add all the numbers together, and all the variables

-(+0.75x)*3x+50*3x+2=0

We multiply parentheses

-0x^2+50*3x+2=0

Wy multiply elements

-0x^2+150x+2=0

We add all the numbers together, and all the variables

-1x^2+150x+2=0

a = -1; b = 150; c = +2;
Δ = b2-4ac
Δ = 1502-4·(-1)·2
Δ = 22508
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:

$\sqrt{\Delta}=\sqrt{22508}=\sqrt{4*5627}=\sqrt{4}*\sqrt{5627}=2\sqrt{5627}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-2\sqrt{5627}}{2*-1}=\frac{-150-2\sqrt{5627}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+2\sqrt{5627}}{2*-1}=\frac{-150+2\sqrt{5627}}{-2}
$