51/2x+2=4x-2

Solution for 51/2x+2=4x-2 equation:

51/2x+2=4x-2

We move all terms to the left:

51/2x+2-(4x-2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

51/2x-4x+2+2=0

We multiply all the terms by the denominator


-4x*2x+2*2x+2*2x+51=0

Wy multiply elements

-8x^2+4x+4x+51=0

We add all the numbers together, and all the variables

-8x^2+8x+51=0

a = -8; b = 8; c = +51;
Δ = b2-4ac
Δ = 82-4·(-8)·51
Δ = 1696
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:

$\sqrt{\Delta}=\sqrt{1696}=\sqrt{16*106}=\sqrt{16}*\sqrt{106}=4\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{106}}{2*-8}=\frac{-8-4\sqrt{106}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{106}}{2*-8}=\frac{-8+4\sqrt{106}}{-16}
$