x+3/7x=70

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

x+3/7x=70

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


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}
$