-2+3/2x+8x=-14

Solution for -2+3/2x+8x=-14 equation:

-2+3/2x+8x=-14

We move all terms to the left:

-2+3/2x+8x-(-14)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

8x+3/2x+12=0

We multiply all the terms by the denominator


8x*2x+12*2x+3=0

Wy multiply elements

16x^2+24x+3=0

a = 16; b = 24; c = +3;
Δ = b2-4ac
Δ = 242-4·16·3
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{6}}{2*16}=\frac{-24-8\sqrt{6}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{6}}{2*16}=\frac{-24+8\sqrt{6}}{32}
$