1/2x+2=4/5x-5

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Solution for 1/2x+2=4/5x-5 equation:



1/2x+2=4/5x-5
We move all terms to the left:
1/2x+2-(4/5x-5)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 5x-5)!=0
x∈R
We get rid of parentheses
1/2x-4/5x+5+2=0
We calculate fractions
5x/10x^2+(-8x)/10x^2+5+2=0
We add all the numbers together, and all the variables
5x/10x^2+(-8x)/10x^2+7=0
We multiply all the terms by the denominator
5x+(-8x)+7*10x^2=0
Wy multiply elements
70x^2+5x+(-8x)=0
We get rid of parentheses
70x^2+5x-8x=0
We add all the numbers together, and all the variables
70x^2-3x=0
a = 70; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·70·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*70}=\frac{0}{140} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*70}=\frac{6}{140} =3/70 $

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