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15/x+1200=30x+500
We move all terms to the left:
15/x+1200-(30x+500)=0
Domain of the equation: x!=0We get rid of parentheses
x∈R
15/x-30x-500+1200=0
We multiply all the terms by the denominator
-30x*x-500*x+1200*x+15=0
We add all the numbers together, and all the variables
700x-30x*x+15=0
Wy multiply elements
-30x^2+700x+15=0
a = -30; b = 700; c = +15;
Δ = b2-4ac
Δ = 7002-4·(-30)·15
Δ = 491800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{491800}=\sqrt{100*4918}=\sqrt{100}*\sqrt{4918}=10\sqrt{4918}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(700)-10\sqrt{4918}}{2*-30}=\frac{-700-10\sqrt{4918}}{-60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(700)+10\sqrt{4918}}{2*-30}=\frac{-700+10\sqrt{4918}}{-60} $
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