3b^2-22-2b+55=232

Solution for 3b^2-22-2b+55=232 equation:

3b^2-22-2b+55=232

We move all terms to the left:

3b^2-22-2b+55-(232)=0

We add all the numbers together, and all the variables

3b^2-2b-199=0

a = 3; b = -2; c = -199;
Δ = b2-4ac
Δ = -22-4·3·(-199)
Δ = 2392
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2392}=\sqrt{4*598}=\sqrt{4}*\sqrt{598}=2\sqrt{598}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{598}}{2*3}=\frac{2-2\sqrt{598}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{598}}{2*3}=\frac{2+2\sqrt{598}}{6}
$