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

Wy multiply elements

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

We add all the numbers together, and all the variables

14x^2-1190x+3=0

a = 14; b = -1190; c = +3;
Δ = b2-4ac
Δ = -11902-4·14·3
Δ = 1415932
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:

$\sqrt{\Delta}=\sqrt{1415932}=\sqrt{4*353983}=\sqrt{4}*\sqrt{353983}=2\sqrt{353983}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1190)-2\sqrt{353983}}{2*14}=\frac{1190-2\sqrt{353983}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1190)+2\sqrt{353983}}{2*14}=\frac{1190+2\sqrt{353983}}{28}
$