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

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



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

We move all terms to the left:

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



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R





Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



We calculate fractions


15x/20x^2+(8x+3)/20x^2-180=0

We multiply all the terms by the denominator


15x+(8x+3)-180*20x^2=0

Wy multiply elements

-3600x^2+15x+(8x+3)=0

We get rid of parentheses

-3600x^2+15x+8x+3=0

We add all the numbers together, and all the variables

-3600x^2+23x+3=0

a = -3600; b = 23; c = +3;
Δ = b2-4ac
Δ = 232-4·(-3600)·3
Δ = 43729
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{-(23)-\sqrt{43729}}{2*-3600}=\frac{-23-\sqrt{43729}}{-7200}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{43729}}{2*-3600}=\frac{-23+\sqrt{43729}}{-7200}
$

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