15x-19=1/2x

Solution for 15x-19=1/2x equation:

15x-19=1/2x

We move all terms to the left:

15x-19-(1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

15x-(+1/2x)-19=0

We get rid of parentheses

15x-1/2x-19=0

We multiply all the terms by the denominator


15x*2x-19*2x-1=0

Wy multiply elements

30x^2-38x-1=0

a = 30; b = -38; c = -1;
Δ = b2-4ac
Δ = -382-4·30·(-1)
Δ = 1564
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:

$\sqrt{\Delta}=\sqrt{1564}=\sqrt{4*391}=\sqrt{4}*\sqrt{391}=2\sqrt{391}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{391}}{2*30}=\frac{38-2\sqrt{391}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{391}}{2*30}=\frac{38+2\sqrt{391}}{60}
$