X-38+1/3x+19+3x-61=180

Solution for X-38+1/3x+19+3x-61=180 equation:

X-38+1/3X+19+3X-61=180

We move all terms to the left:

X-38+1/3X+19+3X-61-(180)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

4X+1/3X-260=0

We multiply all the terms by the denominator


4X*3X-260*3X+1=0

Wy multiply elements

12X^2-780X+1=0

a = 12; b = -780; c = +1;
Δ = b2-4ac
Δ = -7802-4·12·1
Δ = 608352
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:

$\sqrt{\Delta}=\sqrt{608352}=\sqrt{16*38022}=\sqrt{16}*\sqrt{38022}=4\sqrt{38022}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-780)-4\sqrt{38022}}{2*12}=\frac{780-4\sqrt{38022}}{24}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-780)+4\sqrt{38022}}{2*12}=\frac{780+4\sqrt{38022}}{24}
$