-3/5x-7/20x+1/4=-56

Solution for -3/5x-7/20x+1/4=-56 equation:

-3/5x-7/20x+1/4=-56

We move all terms to the left:

-3/5x-7/20x+1/4-(-56)=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

-3/5x-7/20x+56+1/4=0

We calculate fractions


200x^2/1600x^2+(-960x)/1600x^2+(-560x)/1600x^2+56=0

We multiply all the terms by the denominator


200x^2+(-960x)+(-560x)+56*1600x^2=0

Wy multiply elements

200x^2+89600x^2+(-960x)+(-560x)=0

We get rid of parentheses

200x^2+89600x^2-960x-560x=0

We add all the numbers together, and all the variables

89800x^2-1520x=0

a = 89800; b = -1520; c = 0;
Δ = b2-4ac
Δ = -15202-4·89800·0
Δ = 2310400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2310400}=1520$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1520)-1520}{2*89800}=\frac{0}{179600}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1520)+1520}{2*89800}=\frac{3040}{179600}
=38/2245
$