3/4x+0.2(1/4x)+52=x

Solution for 3/4x+0.2(1/4x)+52=x equation:

3/4x+0.2(1/4x)+52=x

We move all terms to the left:

3/4x+0.2(1/4x)+52-(x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x+0.2(+1/4x)-x+52=0

We add all the numbers together, and all the variables

-1x+3/4x+0.2(+1/4x)+52=0

We multiply parentheses

-1x+3/4x+0.2x+52=0

We multiply all the terms by the denominator


-1x*4x+(0.2x)*4x+52*4x+3=0

We add all the numbers together, and all the variables

-1x*4x+(+0.2x)*4x+52*4x+3=0

We multiply parentheses

0x^2-1x*4x+52*4x+3=0

Wy multiply elements

0x^2-4x^2+208x+3=0

We add all the numbers together, and all the variables

-3x^2+208x+3=0

a = -3; b = 208; c = +3;
Δ = b2-4ac
Δ = 2082-4·(-3)·3
Δ = 43300
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:

$\sqrt{\Delta}=\sqrt{43300}=\sqrt{100*433}=\sqrt{100}*\sqrt{433}=10\sqrt{433}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(208)-10\sqrt{433}}{2*-3}=\frac{-208-10\sqrt{433}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(208)+10\sqrt{433}}{2*-3}=\frac{-208+10\sqrt{433}}{-6}
$