4/14x+x=780

Solution for 4/14x+x=780 equation:

4/14x+x=780

We move all terms to the left:

4/14x+x-(780)=0


Domain of the equation: 14x!=0

x!=0/14

x!=0

x∈R


We add all the numbers together, and all the variables

x+4/14x-780=0

We multiply all the terms by the denominator


x*14x-780*14x+4=0

Wy multiply elements

14x^2-10920x+4=0

a = 14; b = -10920; c = +4;
Δ = b2-4ac
Δ = -109202-4·14·4
Δ = 119246176
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:

$\sqrt{\Delta}=\sqrt{119246176}=\sqrt{16*7452886}=\sqrt{16}*\sqrt{7452886}=4\sqrt{7452886}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10920)-4\sqrt{7452886}}{2*14}=\frac{10920-4\sqrt{7452886}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10920)+4\sqrt{7452886}}{2*14}=\frac{10920+4\sqrt{7452886}}{28}
$