X/10x=30+7x

Solution for X/10x=30+7x equation:

X/10X=30+7X

We move all terms to the left:

X/10X-(30+7X)=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-(7X+30)=0

We get rid of parentheses

X/10X-7X-30=0

We multiply all the terms by the denominator


X-7X*10X-30*10X=0

Wy multiply elements

-70X^2+X-300X=0

We add all the numbers together, and all the variables

-70X^2-299X=0

a = -70; b = -299; c = 0;
Δ = b2-4ac
Δ = -2992-4·(-70)·0
Δ = 89401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{89401}=299$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-299)-299}{2*-70}=\frac{0}{-140}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-299)+299}{2*-70}=\frac{598}{-140}
=-4+19/70
$