(3x-30)+(x+30)+(1/5x+54)=180

Solution for (3x-30)+(x+30)+(1/5x+54)=180 equation:

(3x-30)+(x+30)+(1/5x+54)=180

We move all terms to the left:

(3x-30)+(x+30)+(1/5x+54)-(180)=0


Domain of the equation: 5x+54)!=0

x∈R


We get rid of parentheses

3x+x+1/5x-30+30+54-180=0

We multiply all the terms by the denominator


3x*5x+x*5x-30*5x+30*5x+54*5x-180*5x+1=0

Wy multiply elements

15x^2+5x^2-150x+150x+270x-900x+1=0

We add all the numbers together, and all the variables

20x^2-630x+1=0

a = 20; b = -630; c = +1;
Δ = b2-4ac
Δ = -6302-4·20·1
Δ = 396820
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:

$\sqrt{\Delta}=\sqrt{396820}=\sqrt{4*99205}=\sqrt{4}*\sqrt{99205}=2\sqrt{99205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-2\sqrt{99205}}{2*20}=\frac{630-2\sqrt{99205}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+2\sqrt{99205}}{2*20}=\frac{630+2\sqrt{99205}}{40}
$