200/x=5x+30

Solution for 200/x=5x+30 equation:

200/x=5x+30

We move all terms to the left:

200/x-(5x+30)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

200/x-5x-30=0

We multiply all the terms by the denominator


-5x*x-30*x+200=0

We add all the numbers together, and all the variables

-30x-5x*x+200=0

Wy multiply elements

-5x^2-30x+200=0

a = -5; b = -30; c = +200;
Δ = b2-4ac
Δ = -302-4·(-5)·200
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-70}{2*-5}=\frac{-40}{-10}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+70}{2*-5}=\frac{100}{-10}
=-10
$