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(180-x)=2/3x
We move all terms to the left:
(180-x)-(2/3x)=0
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(-1x+180)-(+2/3x)=0
We get rid of parentheses
-1x-2/3x+180=0
We multiply all the terms by the denominator
-1x*3x+180*3x-2=0
Wy multiply elements
-3x^2+540x-2=0
a = -3; b = 540; c = -2;
Δ = b2-4ac
Δ = 5402-4·(-3)·(-2)
Δ = 291576
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{291576}=\sqrt{4*72894}=\sqrt{4}*\sqrt{72894}=2\sqrt{72894}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(540)-2\sqrt{72894}}{2*-3}=\frac{-540-2\sqrt{72894}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(540)+2\sqrt{72894}}{2*-3}=\frac{-540+2\sqrt{72894}}{-6} $
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