1/22x-4=2x-5

Solution for 1/22x-4=2x-5 equation:

1/22x-4=2x-5

We move all terms to the left:

1/22x-4-(2x-5)=0


Domain of the equation: 22x!=0

x!=0/22

x!=0

x∈R


We get rid of parentheses

1/22x-2x+5-4=0

We multiply all the terms by the denominator


-2x*22x+5*22x-4*22x+1=0

Wy multiply elements

-44x^2+110x-88x+1=0

We add all the numbers together, and all the variables

-44x^2+22x+1=0

a = -44; b = 22; c = +1;
Δ = b2-4ac
Δ = 222-4·(-44)·1
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{165}}{2*-44}=\frac{-22-2\sqrt{165}}{-88}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{165}}{2*-44}=\frac{-22+2\sqrt{165}}{-88}
$