6x2=x+222

Solution for 6x2=x+222 equation:

6x^2=x+222

We move all terms to the left:

6x^2-(x+222)=0

We get rid of parentheses

6x^2-x-222=0

We add all the numbers together, and all the variables

6x^2-1x-222=0

a = 6; b = -1; c = -222;
Δ = b2-4ac
Δ = -12-4·6·(-222)
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-73}{2*6}=\frac{-72}{12}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+73}{2*6}=\frac{74}{12}
=6+1/6
$