19/2x=-57/10x+152

Solution for 19/2x=-57/10x+152 equation:

19/2x=-57/10x+152

We move all terms to the left:

19/2x-(-57/10x+152)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 10x+152)!=0

x∈R


We get rid of parentheses

19/2x+57/10x-152=0

We calculate fractions


190x/20x^2+114x/20x^2-152=0

We multiply all the terms by the denominator


190x+114x-152*20x^2=0

We add all the numbers together, and all the variables

304x-152*20x^2=0

Wy multiply elements

-3040x^2+304x=0

a = -3040; b = 304; c = 0;
Δ = b2-4ac
Δ = 3042-4·(-3040)·0
Δ = 92416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{92416}=304$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(304)-304}{2*-3040}=\frac{-608}{-6080}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(304)+304}{2*-3040}=\frac{0}{-6080}
=0
$