x+3/X+(x-10)=180

Solution for x+3/X+(x-10)=180 equation:

x+3/x+(x-10)=180

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-190x+x*x+x*x+3=0

Wy multiply elements

x^2+x^2-190x+3=0

We add all the numbers together, and all the variables

2x^2-190x+3=0

a = 2; b = -190; c = +3;
Δ = b2-4ac
Δ = -1902-4·2·3
Δ = 36076
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:

$\sqrt{\Delta}=\sqrt{36076}=\sqrt{4*9019}=\sqrt{4}*\sqrt{9019}=2\sqrt{9019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-190)-2\sqrt{9019}}{2*2}=\frac{190-2\sqrt{9019}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-190)+2\sqrt{9019}}{2*2}=\frac{190+2\sqrt{9019}}{4}
$