-21x=1/2x-11

Solution for -21x=1/2x-11 equation:

-21x=1/2x-11

We move all terms to the left:

-21x-(1/2x-11)=0


Domain of the equation: 2x-11)!=0

x∈R


We get rid of parentheses

-21x-1/2x+11=0

We multiply all the terms by the denominator


-21x*2x+11*2x-1=0

Wy multiply elements

-42x^2+22x-1=0

a = -42; b = 22; c = -1;
Δ = b2-4ac
Δ = 222-4·(-42)·(-1)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{79}}{2*-42}=\frac{-22-2\sqrt{79}}{-84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{79}}{2*-42}=\frac{-22+2\sqrt{79}}{-84}
$