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

Solution for -3x-7=1/2x+0 equation:

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

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-3x-1/2x-7=0

We multiply all the terms by the denominator


-3x*2x-7*2x-1=0

Wy multiply elements

-6x^2-14x-1=0

a = -6; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·(-6)·(-1)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{43}}{2*-6}=\frac{14-2\sqrt{43}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{43}}{2*-6}=\frac{14+2\sqrt{43}}{-12}
$