1/4x+2+1/4x=4+5/10x+3

Solution for 1/4x+2+1/4x=4+5/10x+3 equation:

1/4x+2+1/4x=4+5/10x+3

We move all terms to the left:

1/4x+2+1/4x-(4+5/10x+3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 10x+3)!=0

x∈R


We add all the numbers together, and all the variables

1/4x+1/4x-(5/10x+7)+2=0

We get rid of parentheses

1/4x+1/4x-5/10x-7+2=0

We calculate fractions


(10x+1)/40x^2+(-20x)/40x^2-7+2=0

We add all the numbers together, and all the variables

(10x+1)/40x^2+(-20x)/40x^2-5=0

We multiply all the terms by the denominator


(10x+1)+(-20x)-5*40x^2=0

Wy multiply elements

-200x^2+(10x+1)+(-20x)=0

We get rid of parentheses

-200x^2+10x-20x+1=0

We add all the numbers together, and all the variables

-200x^2-10x+1=0

a = -200; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·(-200)·1
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-30}{2*-200}=\frac{-20}{-400}
=1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+30}{2*-200}=\frac{40}{-400}
=-1/10
$