14/2+x=12/2x+3

Solution for 14/2+x=12/2x+3 equation:

14/2+x=12/2x+3

We move all terms to the left:

14/2+x-(12/2x+3)=0


Domain of the equation: 2x+3)!=0

x∈R


We add all the numbers together, and all the variables

x-(12/2x+3)+7=0

We get rid of parentheses

x-12/2x-3+7=0

We multiply all the terms by the denominator


x*2x-3*2x+7*2x-12=0

Wy multiply elements

2x^2-6x+14x-12=0

We add all the numbers together, and all the variables

2x^2+8x-12=0

a = 2; b = 8; c = -12;
Δ = b2-4ac
Δ = 82-4·2·(-12)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{10}}{2*2}=\frac{-8-4\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{10}}{2*2}=\frac{-8+4\sqrt{10}}{4}
$