90=2x+700/x

Solution for 90=2x+700/x equation:

90=2x+700/x

We move all terms to the left:

90-(2x+700/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+700/x)+90=0

We get rid of parentheses

-2x-700/x+90=0

We multiply all the terms by the denominator


-2x*x+90*x-700=0

We add all the numbers together, and all the variables

90x-2x*x-700=0

Wy multiply elements

-2x^2+90x-700=0

a = -2; b = 90; c = -700;
Δ = b2-4ac
Δ = 902-4·(-2)·(-700)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-50}{2*-2}=\frac{-140}{-4}
=+35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+50}{2*-2}=\frac{-40}{-4}
=+10
$