3/7x+x=180

Solution for 3/7x+x=180 equation:

3/7x+x=180

We move all terms to the left:

3/7x+x-(180)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/7x-180=0

We multiply all the terms by the denominator


x*7x-180*7x+3=0

Wy multiply elements

7x^2-1260x+3=0

a = 7; b = -1260; c = +3;
Δ = b2-4ac
Δ = -12602-4·7·3
Δ = 1587516
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:

$\sqrt{\Delta}=\sqrt{1587516}=\sqrt{4*396879}=\sqrt{4}*\sqrt{396879}=2\sqrt{396879}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1260)-2\sqrt{396879}}{2*7}=\frac{1260-2\sqrt{396879}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1260)+2\sqrt{396879}}{2*7}=\frac{1260+2\sqrt{396879}}{14}
$