X+13+10/y+8+35=180

Solution for X+13+10/y+8+35=180 equation:

X+13+10/X+8+35=180

We move all terms to the left:

X+13+10/X+8+35-(180)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X+10/X-124=0

We multiply all the terms by the denominator


X*X-124*X+10=0

We add all the numbers together, and all the variables

-124X+X*X+10=0

Wy multiply elements

X^2-124X+10=0

a = 1; b = -124; c = +10;
Δ = b2-4ac
Δ = -1242-4·1·10
Δ = 15336
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:

$\sqrt{\Delta}=\sqrt{15336}=\sqrt{36*426}=\sqrt{36}*\sqrt{426}=6\sqrt{426}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-124)-6\sqrt{426}}{2*1}=\frac{124-6\sqrt{426}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-124)+6\sqrt{426}}{2*1}=\frac{124+6\sqrt{426}}{2}
$