3/2x+4+3/2x+4+1/5x+9=180

Solution for 3/2x+4+3/2x+4+1/5x+9=180 equation:

3/2x+4+3/2x+4+1/5x+9=180

We move all terms to the left:

3/2x+4+3/2x+4+1/5x+9-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x+3/2x+1/5x-163=0

We calculate fractions


(15x+3)/10x^2+2x/10x^2-163=0

We multiply all the terms by the denominator


(15x+3)+2x-163*10x^2=0

We add all the numbers together, and all the variables

2x+(15x+3)-163*10x^2=0

Wy multiply elements

-1630x^2+2x+(15x+3)=0

We get rid of parentheses

-1630x^2+2x+15x+3=0

We add all the numbers together, and all the variables

-1630x^2+17x+3=0

a = -1630; b = 17; c = +3;
Δ = b2-4ac
Δ = 172-4·(-1630)·3
Δ = 19849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{19849}}{2*-1630}=\frac{-17-\sqrt{19849}}{-3260}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{19849}}{2*-1630}=\frac{-17+\sqrt{19849}}{-3260}
$