24-5x/x-2+8x-49/4+x=28/x-2-13

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Solution for 24-5x/x-2+8x-49/4+x=28/x-2-13 equation:



24-5x/x-2+8x-49/4+x=28/x-2-13
We move all terms to the left:
24-5x/x-2+8x-49/4+x-(28/x-2-13)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: x-2-13)!=0
We move all terms containing x to the left, all other terms to the right
x-13)!=2
x∈R
We add all the numbers together, and all the variables
-5x/x+8x+x-(28/x-15)+24-2-49/4=0
We add all the numbers together, and all the variables
9x-5x/x-(28/x-15)+22-49/4=0
We get rid of parentheses
9x-5x/x-28/x+15+22-49/4=0
We calculate fractions
9x+(-5x-112)/4x+(-49x)/4x+15+22=0
We add all the numbers together, and all the variables
9x+(-5x-112)/4x+(-49x)/4x+37=0
We multiply all the terms by the denominator
9x*4x+(-5x-112)+(-49x)+37*4x=0
Wy multiply elements
36x^2+(-5x-112)+(-49x)+148x=0
We get rid of parentheses
36x^2-5x-49x+148x-112=0
We add all the numbers together, and all the variables
36x^2+94x-112=0
a = 36; b = 94; c = -112;
Δ = b2-4ac
Δ = 942-4·36·(-112)
Δ = 24964
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24964}=158$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(94)-158}{2*36}=\frac{-252}{72} =-3+1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(94)+158}{2*36}=\frac{64}{72} =8/9 $

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