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15/x+19-12x=5
We move all terms to the left:
15/x+19-12x-(5)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
-12x+15/x+14=0
We multiply all the terms by the denominator
-12x*x+14*x+15=0
We add all the numbers together, and all the variables
14x-12x*x+15=0
Wy multiply elements
-12x^2+14x+15=0
a = -12; b = 14; c = +15;
Δ = b2-4ac
Δ = 142-4·(-12)·15
Δ = 916
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{229}}{2*-12}=\frac{-14-2\sqrt{229}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{229}}{2*-12}=\frac{-14+2\sqrt{229}}{-24} $
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