x2+x/3=84

Solution for x2+x/3=84 equation:

x2+x/3=84

We move all terms to the left:

x2+x/3-(84)=0

We add all the numbers together, and all the variables

x^2+x/3-84=0

We multiply all the terms by the denominator


x^2*3+x-84*3=0

We add all the numbers together, and all the variables

x^2*3+x-252=0

Wy multiply elements

3x^2+x-252=0

a = 3; b = 1; c = -252;
Δ = b2-4ac
Δ = 12-4·3·(-252)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-55}{2*3}=\frac{-56}{6}
=-9+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+55}{2*3}=\frac{54}{6}
=9
$