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

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
$