x+x-135+1/10x=180

Solution for x+x-135+1/10x=180 equation:

x+x-135+1/10x=180

We move all terms to the left:

x+x-135+1/10x-(180)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/10x-315=0

We multiply all the terms by the denominator


2x*10x-315*10x+1=0

Wy multiply elements

20x^2-3150x+1=0

a = 20; b = -3150; c = +1;
Δ = b2-4ac
Δ = -31502-4·20·1
Δ = 9922420
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:

$\sqrt{\Delta}=\sqrt{9922420}=\sqrt{4*2480605}=\sqrt{4}*\sqrt{2480605}=2\sqrt{2480605}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3150)-2\sqrt{2480605}}{2*20}=\frac{3150-2\sqrt{2480605}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3150)+2\sqrt{2480605}}{2*20}=\frac{3150+2\sqrt{2480605}}{40}
$