420+x+112/x=8.3

Solution for 420+x+112/x=8.3 equation:

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!=0

x∈R


We add all the numbers together, and all the variables

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}
$