4x+6=5/2x+12

Solution for 4x+6=5/2x+12 equation:

4x+6=5/2x+12

We move all terms to the left:

4x+6-(5/2x+12)=0


Domain of the equation: 2x+12)!=0

x∈R


We get rid of parentheses

4x-5/2x-12+6=0

We multiply all the terms by the denominator


4x*2x-12*2x+6*2x-5=0

Wy multiply elements

8x^2-24x+12x-5=0

We add all the numbers together, and all the variables

8x^2-12x-5=0

a = 8; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·8·(-5)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{19}}{2*8}=\frac{12-4\sqrt{19}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{19}}{2*8}=\frac{12+4\sqrt{19}}{16}
$