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

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

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

We move all terms to the left:

-1/2x+7x-2-(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

7x-1/2x-23=0

We multiply all the terms by the denominator


7x*2x-23*2x-1=0

Wy multiply elements

14x^2-46x-1=0

a = 14; b = -46; c = -1;
Δ = b2-4ac
Δ = -462-4·14·(-1)
Δ = 2172
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:

$\sqrt{\Delta}=\sqrt{2172}=\sqrt{4*543}=\sqrt{4}*\sqrt{543}=2\sqrt{543}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{543}}{2*14}=\frac{46-2\sqrt{543}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{543}}{2*14}=\frac{46+2\sqrt{543}}{28}
$