-3/5x-7/10x+1/2=-56

Solution for -3/5x-7/10x+1/2=-56 equation:

-3/5x-7/10x+1/2=-56

We move all terms to the left:

-3/5x-7/10x+1/2-(-56)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

-3/5x-7/10x+56+1/2=0

We calculate fractions


50x^2/200x^2+(-120x)/200x^2+(-140x)/200x^2+56=0

We multiply all the terms by the denominator


50x^2+(-120x)+(-140x)+56*200x^2=0

Wy multiply elements

50x^2+11200x^2+(-120x)+(-140x)=0

We get rid of parentheses

50x^2+11200x^2-120x-140x=0

We add all the numbers together, and all the variables

11250x^2-260x=0

a = 11250; b = -260; c = 0;
Δ = b2-4ac
Δ = -2602-4·11250·0
Δ = 67600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{67600}=260$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-260)-260}{2*11250}=\frac{0}{22500}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-260)+260}{2*11250}=\frac{520}{22500}
=26/1125
$