-2b2-11b=-114+3b

Solution for -2b2-11b=-114+3b equation:

-2b^2-11b=-114+3b

We move all terms to the left:

-2b^2-11b-(-114+3b)=0

We add all the numbers together, and all the variables

-2b^2-11b-(3b-114)=0

We get rid of parentheses

-2b^2-11b-3b+114=0

We add all the numbers together, and all the variables

-2b^2-14b+114=0

a = -2; b = -14; c = +114;
Δ = b2-4ac
Δ = -142-4·(-2)·114
Δ = 1108
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:

$\sqrt{\Delta}=\sqrt{1108}=\sqrt{4*277}=\sqrt{4}*\sqrt{277}=2\sqrt{277}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{277}}{2*-2}=\frac{14-2\sqrt{277}}{-4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{277}}{2*-2}=\frac{14+2\sqrt{277}}{-4}
$