8x-5/x=5x-12.5

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Solution for 8x-5/x=5x-12.5 equation:



8x-5/x=5x-12.5
We move all terms to the left:
8x-5/x-(5x-12.5)=0
Domain of the equation: x!=0
x∈R
We get rid of parentheses
8x-5/x-5x+12.5=0
We multiply all the terms by the denominator
8x*x-5x*x+(12.5)*x-5=0
We multiply parentheses
8x*x-5x*x+12.5x-5=0
Wy multiply elements
8x^2-5x^2+12.5x-5=0
We add all the numbers together, and all the variables
3x^2+12.5x-5=0
a = 3; b = 12.5; c = -5;
Δ = b2-4ac
Δ = 12.52-4·3·(-5)
Δ = 216.25
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{-(12.5)-\sqrt{216.25}}{2*3}=\frac{-12.5-\sqrt{216.25}}{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12.5)+\sqrt{216.25}}{2*3}=\frac{-12.5+\sqrt{216.25}}{6} $

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