X/10x-4x=35+x

Solution for X/10x-4x=35+x equation:

X/10X-4X=35+X

We move all terms to the left:

X/10X-4X-(35+X)=0


Domain of the equation: 10X!=0

X!=0/10

X!=0

X∈R


We add all the numbers together, and all the variables

X/10X-4X-(X+35)=0

We add all the numbers together, and all the variables

-4X+X/10X-(X+35)=0

We get rid of parentheses

-4X+X/10X-X-35=0

We multiply all the terms by the denominator


-4X*10X+X-X*10X-35*10X=0

We add all the numbers together, and all the variables

X-4X*10X-X*10X-35*10X=0

Wy multiply elements

-40X^2-10X^2+X-350X=0

We add all the numbers together, and all the variables

-50X^2-349X=0

a = -50; b = -349; c = 0;
Δ = b2-4ac
Δ = -3492-4·(-50)·0
Δ = 121801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121801}=349$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-349)-349}{2*-50}=\frac{0}{-100}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-349)+349}{2*-50}=\frac{698}{-100}
=-6+49/50
$