x+3/x+x+10=430

Solution for x+3/x+x+10=430 equation:

x+3/x+x+10=430

We move all terms to the left:

x+3/x+x+10-(430)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x+3/x-420=0

We multiply all the terms by the denominator


2x*x-420*x+3=0

We add all the numbers together, and all the variables

-420x+2x*x+3=0

Wy multiply elements

2x^2-420x+3=0

a = 2; b = -420; c = +3;
Δ = b2-4ac
Δ = -4202-4·2·3
Δ = 176376
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:

$\sqrt{\Delta}=\sqrt{176376}=\sqrt{4*44094}=\sqrt{4}*\sqrt{44094}=2\sqrt{44094}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-2\sqrt{44094}}{2*2}=\frac{420-2\sqrt{44094}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+2\sqrt{44094}}{2*2}=\frac{420+2\sqrt{44094}}{4}
$