4x+19=1/2x

Solution for 4x+19=1/2x equation:

4x+19=1/2x

We move all terms to the left:

4x+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

4x-(+1/2x)+19=0

We get rid of parentheses

4x-1/2x+19=0

We multiply all the terms by the denominator


4x*2x+19*2x-1=0

Wy multiply elements

8x^2+38x-1=0

a = 8; b = 38; c = -1;
Δ = b2-4ac
Δ = 382-4·8·(-1)
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-6\sqrt{41}}{2*8}=\frac{-38-6\sqrt{41}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+6\sqrt{41}}{2*8}=\frac{-38+6\sqrt{41}}{16}
$