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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5b^2-11b+114=0

a = -5; b = -11; c = +114;
Δ = b2-4ac
Δ = -112-4·(-5)·114
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-49}{2*-5}=\frac{-38}{-10}
=3+4/5
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+49}{2*-5}=\frac{60}{-10}
=-6
$