X/(10-3)=5(12x)/(10x)

Solution for X/(10-3)=5(12x)/(10x) equation:

X/(10-3)=5(12X)/(10X)

We move all terms to the left:

X/(10-3)-(5(12X)/(10X))=0


Domain of the equation: 10X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X/7-(+512X/10X)=0

We get rid of parentheses

X/7-512X/10X=0

We calculate fractions


10X^2/70X+(-3584X)/70X=0

We multiply all the terms by the denominator


10X^2+(-3584X)=0

We get rid of parentheses

10X^2-3584X=0

a = 10; b = -3584; c = 0;
Δ = b2-4ac
Δ = -35842-4·10·0
Δ = 12845056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12845056}=3584$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3584)-3584}{2*10}=\frac{0}{20}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3584)+3584}{2*10}=\frac{7168}{20}
=358+2/5
$