2/3x+5=30-x

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Solution for 2/3x+5=30-x equation:



2/3x+5=30-x
We move all terms to the left:
2/3x+5-(30-x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
2/3x-(-1x+30)+5=0
We get rid of parentheses
2/3x+1x-30+5=0
We multiply all the terms by the denominator
1x*3x-30*3x+5*3x+2=0
Wy multiply elements
3x^2-90x+15x+2=0
We add all the numbers together, and all the variables
3x^2-75x+2=0
a = 3; b = -75; c = +2;
Δ = b2-4ac
Δ = -752-4·3·2
Δ = 5601
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{-(-75)-\sqrt{5601}}{2*3}=\frac{75-\sqrt{5601}}{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{5601}}{2*3}=\frac{75+\sqrt{5601}}{6} $

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