12x+4=5/2x+2

Solution for 12x+4=5/2x+2 equation:

12x+4=5/2x+2

We move all terms to the left:

12x+4-(5/2x+2)=0


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

x∈R


We get rid of parentheses

12x-5/2x-2+4=0

We multiply all the terms by the denominator


12x*2x-2*2x+4*2x-5=0

Wy multiply elements

24x^2-4x+8x-5=0

We add all the numbers together, and all the variables

24x^2+4x-5=0

a = 24; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·24·(-5)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{31}}{2*24}=\frac{-4-4\sqrt{31}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{31}}{2*24}=\frac{-4+4\sqrt{31}}{48}
$