X/3+x2=14

Solution for X/3+x2=14 equation:

X/3+X2=14

We move all terms to the left:

X/3+X2-(14)=0

We add all the numbers together, and all the variables

X^2+X/3-14=0

We multiply all the terms by the denominator


X^2*3+X-14*3=0

We add all the numbers together, and all the variables

X^2*3+X-42=0

Wy multiply elements

3X^2+X-42=0

a = 3; b = 1; c = -42;
Δ = b2-4ac
Δ = 12-4·3·(-42)
Δ = 505
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{-(1)-\sqrt{505}}{2*3}=\frac{-1-\sqrt{505}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{505}}{2*3}=\frac{-1+\sqrt{505}}{6}
$