180-x=6x(90-x)

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Solution for 180-x=6x(90-x) equation:



180-x=6x(90-x)
We move all terms to the left:
180-x-(6x(90-x))=0
We add all the numbers together, and all the variables
-x-(6x(-1x+90))+180=0
We add all the numbers together, and all the variables
-1x-(6x(-1x+90))+180=0
We calculate terms in parentheses: -(6x(-1x+90)), so:
6x(-1x+90)
We multiply parentheses
-6x^2+540x
Back to the equation:
-(-6x^2+540x)
We get rid of parentheses
6x^2-540x-1x+180=0
We add all the numbers together, and all the variables
6x^2-541x+180=0
a = 6; b = -541; c = +180;
Δ = b2-4ac
Δ = -5412-4·6·180
Δ = 288361
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{-(-541)-\sqrt{288361}}{2*6}=\frac{541-\sqrt{288361}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-541)+\sqrt{288361}}{2*6}=\frac{541+\sqrt{288361}}{12} $

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