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


determiningTheFunctionDomain
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

-11150x^2-20x=0

a = -11150; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-11150)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-11150}=\frac{0}{-22300}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-11150}=\frac{40}{-22300}
=-2/1115
$