10/3x+4+7x-7+5x-1=180

Solution for 10/3x+4+7x-7+5x-1=180 equation:

10/3x+4+7x-7+5x-1=180

We move all terms to the left:

10/3x+4+7x-7+5x-1-(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

12x+10/3x-184=0

We multiply all the terms by the denominator


12x*3x-184*3x+10=0

Wy multiply elements

36x^2-552x+10=0

a = 36; b = -552; c = +10;
Δ = b2-4ac
Δ = -5522-4·36·10
Δ = 303264
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:

$\sqrt{\Delta}=\sqrt{303264}=\sqrt{11664*26}=\sqrt{11664}*\sqrt{26}=108\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-552)-108\sqrt{26}}{2*36}=\frac{552-108\sqrt{26}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-552)+108\sqrt{26}}{2*36}=\frac{552+108\sqrt{26}}{72}
$