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

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

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

We move all terms to the left:

-2+3/2x+8-x-(-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

-1x+3/2x+20=0

We multiply all the terms by the denominator


-1x*2x+20*2x+3=0

Wy multiply elements

-2x^2+40x+3=0

a = -2; b = 40; c = +3;
Δ = b2-4ac
Δ = 402-4·(-2)·3
Δ = 1624
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:

$\sqrt{\Delta}=\sqrt{1624}=\sqrt{4*406}=\sqrt{4}*\sqrt{406}=2\sqrt{406}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{406}}{2*-2}=\frac{-40-2\sqrt{406}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{406}}{2*-2}=\frac{-40+2\sqrt{406}}{-4}
$