-3-7-x=1/2x+2

Solution for -3-7-x=1/2x+2 equation:

-3-7-x=1/2x+2

We move all terms to the left:

-3-7-x-(1/2x+2)=0


Domain of the equation: 2x+2)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(1/2x+2)-10=0

We get rid of parentheses

-1x-1/2x-2-10=0

We multiply all the terms by the denominator


-1x*2x-2*2x-10*2x-1=0

Wy multiply elements

-2x^2-4x-20x-1=0

We add all the numbers together, and all the variables

-2x^2-24x-1=0

a = -2; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·(-2)·(-1)
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{142}}{2*-2}=\frac{24-2\sqrt{142}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{142}}{2*-2}=\frac{24+2\sqrt{142}}{-4}
$