x*3/7x+(x+10)=180

Solution for x*3/7x+(x+10)=180 equation:

x*3/7x+(x+10)=180

We move all terms to the left:

x*3/7x+(x+10)-(180)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

x*3/7x+x+10-180=0

We multiply all the terms by the denominator


x*3+x*7x+10*7x-180*7x=0

Wy multiply elements

7x^2+3x+70x-1260x=0

We add all the numbers together, and all the variables

7x^2-1187x=0

a = 7; b = -1187; c = 0;
Δ = b2-4ac
Δ = -11872-4·7·0
Δ = 1408969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1408969}=1187$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1187)-1187}{2*7}=\frac{0}{14}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1187)+1187}{2*7}=\frac{2374}{14}
=169+4/7
$