X-5+3x+29+2/3x+8=360

Solution for X-5+3x+29+2/3x+8=360 equation:

X-5+3X+29+2/3X+8=360

We move all terms to the left:

X-5+3X+29+2/3X+8-(360)=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+2/3X-328=0

We multiply all the terms by the denominator


4X*3X-328*3X+2=0

Wy multiply elements

12X^2-984X+2=0

a = 12; b = -984; c = +2;
Δ = b2-4ac
Δ = -9842-4·12·2
Δ = 968160
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:

$\sqrt{\Delta}=\sqrt{968160}=\sqrt{16*60510}=\sqrt{16}*\sqrt{60510}=4\sqrt{60510}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-984)-4\sqrt{60510}}{2*12}=\frac{984-4\sqrt{60510}}{24}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-984)+4\sqrt{60510}}{2*12}=\frac{984+4\sqrt{60510}}{24}
$