x=150000+10x/30x

Solution for x=150000+10x/30x equation:

x=150000+10x/30x

We move all terms to the left:

x-(150000+10x/30x)=0


Domain of the equation: 30x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(10x/30x+150000)=0

We get rid of parentheses

x-10x/30x-150000=0

We multiply all the terms by the denominator


x*30x-10x-150000*30x=0

We add all the numbers together, and all the variables

-10x+x*30x-150000*30x=0

Wy multiply elements

30x^2-10x-4500000x=0

We add all the numbers together, and all the variables

30x^2-4500010x=0

a = 30; b = -4500010; c = 0;
Δ = b2-4ac
Δ = -45000102-4·30·0
Δ = 20250090000100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20250090000100}=4500010$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4500010)-4500010}{2*30}=\frac{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4500010)+4500010}{2*30}=\frac{9000020}{60}
=150000+1/3
$