(40000+.7x)/x=150x

Solution for (40000+.7x)/x=150x equation:

(40000+.7x)/x=150x

We move all terms to the left:

(40000+.7x)/x-(150x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

(.7x+40000)/x-150x=0

We add all the numbers together, and all the variables

-150x+(.7x+40000)/x=0

We multiply all the terms by the denominator


-150x*x+(.7x+40000)=0

Wy multiply elements

-150x^2+(.7x+40000)=0

We get rid of parentheses

-150x^2+.7x+40000=0

a = -150; b = .7; c = +40000;
Δ = b2-4ac
Δ = .72-4·(-150)·40000
Δ = 24000000.49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(.7)-\sqrt{24000000.49}}{2*-150}=\frac{-0.7-\sqrt{24000000.49}}{-300}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(.7)+\sqrt{24000000.49}}{2*-150}=\frac{-0.7+\sqrt{24000000.49}}{-300}
$