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

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

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

We move all terms to the left:

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+1/5x-167=0

We calculate fractions


15x/10x^2+2x/10x^2-167=0

We multiply all the terms by the denominator


15x+2x-167*10x^2=0

We add all the numbers together, and all the variables

17x-167*10x^2=0

Wy multiply elements

-1670x^2+17x=0

a = -1670; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-1670)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-1670}=\frac{-34}{-3340}
=17/1670
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-1670}=\frac{0}{-3340}
=0
$