x+4/7x=77

Solution for x+4/7x=77 equation:

x+4/7x=77

We move all terms to the left:

x+4/7x-(77)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


x*7x-77*7x+4=0

Wy multiply elements

7x^2-539x+4=0

a = 7; b = -539; c = +4;
Δ = b2-4ac
Δ = -5392-4·7·4
Δ = 290409
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{-(-539)-\sqrt{290409}}{2*7}=\frac{539-\sqrt{290409}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-539)+\sqrt{290409}}{2*7}=\frac{539+\sqrt{290409}}{14}
$