1/2x-10=-21x+2

Solution for 1/2x-10=-21x+2 equation:

1/2x-10=-21x+2

We move all terms to the left:

1/2x-10-(-21x+2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x+21x-2-10=0

We multiply all the terms by the denominator


21x*2x-2*2x-10*2x+1=0

Wy multiply elements

42x^2-4x-20x+1=0

We add all the numbers together, and all the variables

42x^2-24x+1=0

a = 42; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·42·1
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{102}}{2*42}=\frac{24-2\sqrt{102}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{102}}{2*42}=\frac{24+2\sqrt{102}}{84}
$