51/2x+2=312x+14

Solution for 51/2x+2=312x+14 equation:

51/2x+2=312x+14

We move all terms to the left:

51/2x+2-(312x+14)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

51/2x-312x-14+2=0

We multiply all the terms by the denominator


-312x*2x-14*2x+2*2x+51=0

Wy multiply elements

-624x^2-28x+4x+51=0

We add all the numbers together, and all the variables

-624x^2-24x+51=0

a = -624; b = -24; c = +51;
Δ = b2-4ac
Δ = -242-4·(-624)·51
Δ = 127872
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:

$\sqrt{\Delta}=\sqrt{127872}=\sqrt{576*222}=\sqrt{576}*\sqrt{222}=24\sqrt{222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{222}}{2*-624}=\frac{24-24\sqrt{222}}{-1248}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{222}}{2*-624}=\frac{24+24\sqrt{222}}{-1248}
$