21-3x=1/2x+1

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

21-3x=1/2x+1

We move all terms to the left:

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


Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-6x^2+40x-1=0

a = -6; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·(-6)·(-1)
Δ = 1576
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:

$\sqrt{\Delta}=\sqrt{1576}=\sqrt{4*394}=\sqrt{4}*\sqrt{394}=2\sqrt{394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{394}}{2*-6}=\frac{-40-2\sqrt{394}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{394}}{2*-6}=\frac{-40+2\sqrt{394}}{-12}
$