2x-5-18x=(1/2)(22x+10)

Solution for 2x-5-18x=(1/2)(22x+10) equation:

2x-5-18x=(1/2)(22x+10)

We move all terms to the left:

2x-5-18x-((1/2)(22x+10))=0


Domain of the equation: 2)(22x+10))!=0

x∈R


We add all the numbers together, and all the variables

2x-18x-((+1/2)(22x+10))-5=0

We add all the numbers together, and all the variables

-16x-((+1/2)(22x+10))-5=0

We multiply parentheses ..

-((+22x^2+1/2*10))-16x-5=0

We multiply all the terms by the denominator


-((+22x^2+1-16x*2*10))-5*2*10))=0


We calculate terms in parentheses: -((+22x^2+1-16x*2*10)), so:

(+22x^2+1-16x*2*10)

We get rid of parentheses

22x^2-16x*2*10+1

Wy multiply elements

22x^2-320x*1+1

Wy multiply elements

22x^2-320x+1

Back to the equation:

-(22x^2-320x+1)


We add all the numbers together, and all the variables

-(22x^2-320x+1)=0

We get rid of parentheses

-22x^2+320x-1=0

a = -22; b = 320; c = -1;
Δ = b2-4ac
Δ = 3202-4·(-22)·(-1)
Δ = 102312
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:

$\sqrt{\Delta}=\sqrt{102312}=\sqrt{1764*58}=\sqrt{1764}*\sqrt{58}=42\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320)-42\sqrt{58}}{2*-22}=\frac{-320-42\sqrt{58}}{-44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320)+42\sqrt{58}}{2*-22}=\frac{-320+42\sqrt{58}}{-44}
$