1/5x*5=19-1/2x

Solution for 1/5x*5=19-1/2x equation:

1/5x*5=19-1/2x

We move all terms to the left:

1/5x*5-(19-1/2x)=0


Domain of the equation: 5x*5!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x*5-(-1/2x+19)=0

We get rid of parentheses

1/5x*5+1/2x-19=0

We calculate fractions


2x/100x^2+125x/100x^2-19=0

We multiply all the terms by the denominator


2x+125x-19*100x^2=0

We add all the numbers together, and all the variables

127x-19*100x^2=0

Wy multiply elements

-1900x^2+127x=0

a = -1900; b = 127; c = 0;
Δ = b2-4ac
Δ = 1272-4·(-1900)·0
Δ = 16129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16129}=127$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(127)-127}{2*-1900}=\frac{-254}{-3800}
=127/1900
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(127)+127}{2*-1900}=\frac{0}{-3800}
=0
$