X=-2/3y+60

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Solution for X=-2/3y+60 equation:



X=-2/3X+60
We move all terms to the left:
X-(-2/3X+60)=0
Domain of the equation: 3X+60)!=0
X∈R
We get rid of parentheses
X+2/3X-60=0
We multiply all the terms by the denominator
X*3X-60*3X+2=0
Wy multiply elements
3X^2-180X+2=0
a = 3; b = -180; c = +2;
Δ = b2-4ac
Δ = -1802-4·3·2
Δ = 32376
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:
$\sqrt{\Delta}=\sqrt{32376}=\sqrt{4*8094}=\sqrt{4}*\sqrt{8094}=2\sqrt{8094}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-2\sqrt{8094}}{2*3}=\frac{180-2\sqrt{8094}}{6} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+2\sqrt{8094}}{2*3}=\frac{180+2\sqrt{8094}}{6} $

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