3+1/2x+4=4x-6/2x

Solution for 3+1/2x+4=4x-6/2x equation:

3+1/2x+4=4x-6/2x

We move all terms to the left:

3+1/2x+4-(4x-6/2x)=0


Domain of the equation: 2x!=0

x!=0/2

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

1/2x-(+4x-6/2x)+3+4=0

We add all the numbers together, and all the variables

1/2x-(+4x-6/2x)+7=0

We get rid of parentheses

1/2x-4x+6/2x+7=0

We multiply all the terms by the denominator


-4x*2x+7*2x+1+6=0

We add all the numbers together, and all the variables

-4x*2x+7*2x+7=0

Wy multiply elements

-8x^2+14x+7=0

a = -8; b = 14; c = +7;
Δ = b2-4ac
Δ = 142-4·(-8)·7
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{105}}{2*-8}=\frac{-14-2\sqrt{105}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{105}}{2*-8}=\frac{-14+2\sqrt{105}}{-16}
$