414-3x2=32-81x+22.

Solution for 414-3x2=32-81x+22. equation:

414-3x^2=32-81x+22.

We move all terms to the left:

414-3x^2-(32-81x+22.)=0

We add all the numbers together, and all the variables

-3x^2-(-81x+54)+414=0

We get rid of parentheses

-3x^2+81x-54+414=0

We add all the numbers together, and all the variables

-3x^2+81x+360=0

a = -3; b = 81; c = +360;
Δ = b2-4ac
Δ = 812-4·(-3)·360
Δ = 10881
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:

$\sqrt{\Delta}=\sqrt{10881}=\sqrt{9*1209}=\sqrt{9}*\sqrt{1209}=3\sqrt{1209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-3\sqrt{1209}}{2*-3}=\frac{-81-3\sqrt{1209}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+3\sqrt{1209}}{2*-3}=\frac{-81+3\sqrt{1209}}{-6}
$