B(x)=-3x2+138x-912

Solution for B(x)=-3x2+138x-912 equation:

(B)=-3B^2+138B-912

We move all terms to the left:

(B)-(-3B^2+138B-912)=0

We get rid of parentheses

3B^2-138B+B+912=0

We add all the numbers together, and all the variables

3B^2-137B+912=0

a = 3; b = -137; c = +912;
Δ = b2-4ac
Δ = -1372-4·3·912
Δ = 7825
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:

$\sqrt{\Delta}=\sqrt{7825}=\sqrt{25*313}=\sqrt{25}*\sqrt{313}=5\sqrt{313}$
$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-137)-5\sqrt{313}}{2*3}=\frac{137-5\sqrt{313}}{6}
$
$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-137)+5\sqrt{313}}{2*3}=\frac{137+5\sqrt{313}}{6}
$