1/2x+2=-5/8x-5

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Solution for 1/2x+2=-5/8x-5 equation:



1/2x+2=-5/8x-5
We move all terms to the left:
1/2x+2-(-5/8x-5)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 8x-5)!=0
x∈R
We get rid of parentheses
1/2x+5/8x+5+2=0
We calculate fractions
8x/16x^2+10x/16x^2+5+2=0
We add all the numbers together, and all the variables
8x/16x^2+10x/16x^2+7=0
We multiply all the terms by the denominator
8x+10x+7*16x^2=0
We add all the numbers together, and all the variables
18x+7*16x^2=0
Wy multiply elements
112x^2+18x=0
a = 112; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·112·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*112}=\frac{-36}{224} =-9/56 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*112}=\frac{0}{224} =0 $

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