x-12+2x-122+1/5x+6=180

Solution for x-12+2x-122+1/5x+6=180 equation:

x-12+2x-122+1/5x+6=180

We move all terms to the left:

x-12+2x-122+1/5x+6-(180)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/5x-308=0

We multiply all the terms by the denominator


3x*5x-308*5x+1=0

Wy multiply elements

15x^2-1540x+1=0

a = 15; b = -1540; c = +1;
Δ = b2-4ac
Δ = -15402-4·15·1
Δ = 2371540
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:

$\sqrt{\Delta}=\sqrt{2371540}=\sqrt{4*592885}=\sqrt{4}*\sqrt{592885}=2\sqrt{592885}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1540)-2\sqrt{592885}}{2*15}=\frac{1540-2\sqrt{592885}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1540)+2\sqrt{592885}}{2*15}=\frac{1540+2\sqrt{592885}}{30}
$