7/2x+1=21x

Solution for 7/2x+1=21x equation:

7/2x+1=21x

We move all terms to the left:

7/2x+1-(21x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-21x+7/2x+1=0

We multiply all the terms by the denominator


-21x*2x+1*2x+7=0

Wy multiply elements

-42x^2+2x+7=0

a = -42; b = 2; c = +7;
Δ = b2-4ac
Δ = 22-4·(-42)·7
Δ = 1180
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:

$\sqrt{\Delta}=\sqrt{1180}=\sqrt{4*295}=\sqrt{4}*\sqrt{295}=2\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{295}}{2*-42}=\frac{-2-2\sqrt{295}}{-84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{295}}{2*-42}=\frac{-2+2\sqrt{295}}{-84}
$