X+2/3x=800

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Solution for X+2/3x=800 equation: 



X+2/3X=800

We move all terms to the left:

X+2/3X-(800)=0



Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R



We multiply all the terms by the denominator


X*3X-800*3X+2=0

Wy multiply elements

3X^2-2400X+2=0

a = 3; b = -2400; c = +2;
Δ = b2-4ac
Δ = -24002-4·3·2
Δ = 5759976
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:


$\sqrt{\Delta}=\sqrt{5759976}=\sqrt{4*1439994}=\sqrt{4}*\sqrt{1439994}=2\sqrt{1439994}$


$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2400)-2\sqrt{1439994}}{2*3}=\frac{2400-2\sqrt{1439994}}{6}
$


$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2400)+2\sqrt{1439994}}{2*3}=\frac{2400+2\sqrt{1439994}}{6}
$

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