-3x-1/2x=-21

Solution for -3x-1/2x=-21 equation:

-3x-1/2x=-21

We move all terms to the left:

-3x-1/2x-(-21)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-3x-1/2x+21=0

We multiply all the terms by the denominator


-3x*2x+21*2x-1=0

Wy multiply elements

-6x^2+42x-1=0

a = -6; b = 42; c = -1;
Δ = b2-4ac
Δ = 422-4·(-6)·(-1)
Δ = 1740
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:

$\sqrt{\Delta}=\sqrt{1740}=\sqrt{4*435}=\sqrt{4}*\sqrt{435}=2\sqrt{435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{435}}{2*-6}=\frac{-42-2\sqrt{435}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{435}}{2*-6}=\frac{-42+2\sqrt{435}}{-12}
$