14+2/3+x^2=85

Solution for 14+2/3+x^2=85 equation:

14+2/3+x^2=85

We move all terms to the left:

14+2/3+x^2-(85)=0

determiningTheFunctionDomain
x^2+14-85+2/3=0

We add all the numbers together, and all the variables

x^2-71+2/3=0

We multiply all the terms by the denominator


x^2*3+2-71*3=0

We add all the numbers together, and all the variables

x^2*3-211=0

Wy multiply elements

3x^2-211=0

a = 3; b = 0; c = -211;
Δ = b2-4ac
Δ = 02-4·3·(-211)
Δ = 2532
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:

$\sqrt{\Delta}=\sqrt{2532}=\sqrt{4*633}=\sqrt{4}*\sqrt{633}=2\sqrt{633}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{633}}{2*3}=\frac{0-2\sqrt{633}}{6}
=-\frac{2\sqrt{633}}{6}
=-\frac{\sqrt{633}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{633}}{2*3}=\frac{0+2\sqrt{633}}{6}
=\frac{2\sqrt{633}}{6}
=\frac{\sqrt{633}}{3}
$