(19/3)x=5/2

Solution for (19/3)x=5/2 equation:

(19/3)x=5/2

We move all terms to the left:

(19/3)x-(5/2)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+19/3)x-(+5/2)=0

We multiply parentheses

19x^2-(+5/2)=0

We get rid of parentheses

19x^2-5/2=0

We multiply all the terms by the denominator


19x^2*2-5=0

Wy multiply elements

38x^2-5=0

a = 38; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·38·(-5)
Δ = 760
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{190}}{2*38}=\frac{0-2\sqrt{190}}{76}
=-\frac{2\sqrt{190}}{76}
=-\frac{\sqrt{190}}{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{190}}{2*38}=\frac{0+2\sqrt{190}}{76}
=\frac{2\sqrt{190}}{76}
=\frac{\sqrt{190}}{38}
$