x+2/3x=4812

Solution for x+2/3x=4812 equation:

x+2/3x=4812

We move all terms to the left:

x+2/3x-(4812)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-4812*3x+2=0

Wy multiply elements

3x^2-14436x+2=0

a = 3; b = -14436; c = +2;
Δ = b2-4ac
Δ = -144362-4·3·2
Δ = 208398072
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:

$\sqrt{\Delta}=\sqrt{208398072}=\sqrt{4*52099518}=\sqrt{4}*\sqrt{52099518}=2\sqrt{52099518}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14436)-2\sqrt{52099518}}{2*3}=\frac{14436-2\sqrt{52099518}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14436)+2\sqrt{52099518}}{2*3}=\frac{14436+2\sqrt{52099518}}{6}
$