5/2x+12=2x-2

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

5/2x+12=2x-2

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-4x^2+28x+5=0

a = -4; b = 28; c = +5;
Δ = b2-4ac
Δ = 282-4·(-4)·5
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-12\sqrt{6}}{2*-4}=\frac{-28-12\sqrt{6}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+12\sqrt{6}}{2*-4}=\frac{-28+12\sqrt{6}}{-8}
$