70=2x+400/x

Solution for 70=2x+400/x equation:

70=2x+400/x

We move all terms to the left:

70-(2x+400/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+2x+400/x)+70=0

We get rid of parentheses

-2x-400/x+70=0

We multiply all the terms by the denominator


-2x*x+70*x-400=0

We add all the numbers together, and all the variables

70x-2x*x-400=0

Wy multiply elements

-2x^2+70x-400=0

a = -2; b = 70; c = -400;
Δ = b2-4ac
Δ = 702-4·(-2)·(-400)
Δ = 1700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1700}=\sqrt{100*17}=\sqrt{100}*\sqrt{17}=10\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-10\sqrt{17}}{2*-2}=\frac{-70-10\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+10\sqrt{17}}{2*-2}=\frac{-70+10\sqrt{17}}{-4}
$