30=x+0.2(700)/x+700

Solution for 30=x+0.2(700)/x+700 equation:

30=x+0.2(700)/x+700

We move all terms to the left:

30-(x+0.2(700)/x+700)=0


Domain of the equation: x+700)!=0

x∈R


We get rid of parentheses

-x-0.2700/x-700+30=0

We multiply all the terms by the denominator


-x*x-700*x+30*x-0.2700=0

We add all the numbers together, and all the variables

-670x-x*x-0.27=0

Wy multiply elements

-1x^2-670x-0.27=0

a = -1; b = -670; c = -0.27;
Δ = b2-4ac
Δ = -6702-4·(-1)·(-0.27)
Δ = 448898.92
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{-(-670)-\sqrt{448898.92}}{2*-1}=\frac{670-\sqrt{448898.92}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-670)+\sqrt{448898.92}}{2*-1}=\frac{670+\sqrt{448898.92}}{-2}
$