-4/5x-7/20x+1/4=-72

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Solution for -4/5x-7/20x+1/4=-72 equation:



-4/5x-7/20x+1/4=-72
We move all terms to the left:
-4/5x-7/20x+1/4-(-72)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 20x!=0
x!=0/20
x!=0
x∈R
We add all the numbers together, and all the variables
-4/5x-7/20x+72+1/4=0
We calculate fractions
200x^2/1600x^2+(-1280x)/1600x^2+(-560x)/1600x^2+72=0
We multiply all the terms by the denominator
200x^2+(-1280x)+(-560x)+72*1600x^2=0
Wy multiply elements
200x^2+115200x^2+(-1280x)+(-560x)=0
We get rid of parentheses
200x^2+115200x^2-1280x-560x=0
We add all the numbers together, and all the variables
115400x^2-1840x=0
a = 115400; b = -1840; c = 0;
Δ = b2-4ac
Δ = -18402-4·115400·0
Δ = 3385600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3385600}=1840$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1840)-1840}{2*115400}=\frac{0}{230800} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1840)+1840}{2*115400}=\frac{3680}{230800} =46/2885 $

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