X+1/3x=950

Solution for X+1/3x=950 equation:

X+1/3X=950

We move all terms to the left:

X+1/3X-(950)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-950*3X+1=0

Wy multiply elements

3X^2-2850X+1=0

a = 3; b = -2850; c = +1;
Δ = b2-4ac
Δ = -28502-4·3·1
Δ = 8122488
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:

$\sqrt{\Delta}=\sqrt{8122488}=\sqrt{484*16782}=\sqrt{484}*\sqrt{16782}=22\sqrt{16782}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2850)-22\sqrt{16782}}{2*3}=\frac{2850-22\sqrt{16782}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2850)+22\sqrt{16782}}{2*3}=\frac{2850+22\sqrt{16782}}{6}
$