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420+x+112/x=8.3
We move all terms to the left:
420+x+112/x-(8.3)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
x+112/x+411.7=0
We multiply all the terms by the denominator
x*x+(411.7)*x+112=0
We multiply parentheses
x*x+411.7x+112=0
Wy multiply elements
x^2+411.7x+112=0
a = 1; b = 411.7; c = +112;
Δ = b2-4ac
Δ = 411.72-4·1·112
Δ = 169048.89
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{-(411.7)-\sqrt{169048.89}}{2*1}=\frac{-411.7-\sqrt{169048.89}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(411.7)+\sqrt{169048.89}}{2*1}=\frac{-411.7+\sqrt{169048.89}}{2} $
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