9x(5x-2)-x=8+(4-2x)

Solution for 9x(5x-2)-x=8+(4-2x) equation:

9x(5x-2)-x=8+(4-2x)

We move all terms to the left:

9x(5x-2)-x-(8+(4-2x))=0

We add all the numbers together, and all the variables

9x(5x-2)-x-(8+(-2x+4))=0

We add all the numbers together, and all the variables

-1x+9x(5x-2)-(8+(-2x+4))=0

We multiply parentheses

45x^2-1x-18x-(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

45x^2-19x-(-2x+12)=0

We get rid of parentheses

45x^2-19x+2x-12=0

We add all the numbers together, and all the variables

45x^2-17x-12=0

a = 45; b = -17; c = -12;
Δ = b2-4ac
Δ = -172-4·45·(-12)
Δ = 2449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{2449}}{2*45}=\frac{17-\sqrt{2449}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{2449}}{2*45}=\frac{17+\sqrt{2449}}{90}
$