5x+7=-2/3x+20

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Solution for 5x+7=-2/3x+20 equation:



5x+7=-2/3x+20
We move all terms to the left:
5x+7-(-2/3x+20)=0
Domain of the equation: 3x+20)!=0
x∈R
We get rid of parentheses
5x+2/3x-20+7=0
We multiply all the terms by the denominator
5x*3x-20*3x+7*3x+2=0
Wy multiply elements
15x^2-60x+21x+2=0
We add all the numbers together, and all the variables
15x^2-39x+2=0
a = 15; b = -39; c = +2;
Δ = b2-4ac
Δ = -392-4·15·2
Δ = 1401
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{-(-39)-\sqrt{1401}}{2*15}=\frac{39-\sqrt{1401}}{30} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1401}}{2*15}=\frac{39+\sqrt{1401}}{30} $

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