70=x+3/7x

Solution for 70=x+3/7x equation:

70=x+3/7x

We move all terms to the left:

70-(x+3/7x)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x+3/7x)+70=0

We get rid of parentheses

-x-3/7x+70=0

We multiply all the terms by the denominator


-x*7x+70*7x-3=0

Wy multiply elements

-7x^2+490x-3=0

a = -7; b = 490; c = -3;
Δ = b2-4ac
Δ = 4902-4·(-7)·(-3)
Δ = 240016
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:

$\sqrt{\Delta}=\sqrt{240016}=\sqrt{16*15001}=\sqrt{16}*\sqrt{15001}=4\sqrt{15001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(490)-4\sqrt{15001}}{2*-7}=\frac{-490-4\sqrt{15001}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(490)+4\sqrt{15001}}{2*-7}=\frac{-490+4\sqrt{15001}}{-14}
$