18x(10x-4)-2x=8+(4-2x)

Solution for 18x(10x-4)-2x=8+(4-2x) equation:

18x(10x-4)-2x=8+(4-2x)

We move all terms to the left:

18x(10x-4)-2x-(8+(4-2x))=0

We add all the numbers together, and all the variables

18x(10x-4)-2x-(8+(-2x+4))=0

We add all the numbers together, and all the variables

-2x+18x(10x-4)-(8+(-2x+4))=0

We multiply parentheses

180x^2-2x-72x-(8+(-2x+4))=0


We calculate terms in parentheses: -(8+(-2x+4)), so:

8+(-2x+4)

determiningTheFunctionDomain
(-2x+4)+8

We get rid of parentheses

-2x+4+8

We add all the numbers together, and all the variables

-2x+12

Back to the equation:

-(-2x+12)


We add all the numbers together, and all the variables

180x^2-74x-(-2x+12)=0

We get rid of parentheses

180x^2-74x+2x-12=0

We add all the numbers together, and all the variables

180x^2-72x-12=0

a = 180; b = -72; c = -12;
Δ = b2-4ac
Δ = -722-4·180·(-12)
Δ = 13824
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:

$\sqrt{\Delta}=\sqrt{13824}=\sqrt{2304*6}=\sqrt{2304}*\sqrt{6}=48\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-48\sqrt{6}}{2*180}=\frac{72-48\sqrt{6}}{360}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+48\sqrt{6}}{2*180}=\frac{72+48\sqrt{6}}{360}
$