6x^2+x=216+x

Solution for 6x^2+x=216+x equation:

6x^2+x=216+x

We move all terms to the left:

6x^2+x-(216+x)=0

We add all the numbers together, and all the variables

6x^2+x-(x+216)=0

We get rid of parentheses

6x^2+x-x-216=0

We add all the numbers together, and all the variables

6x^2-216=0

a = 6; b = 0; c = -216;
Δ = b2-4ac
Δ = 02-4·6·(-216)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72}{2*6}=\frac{-72}{12}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72}{2*6}=\frac{72}{12}
=6
$