2b^2+11b-10=12+9b

Solution for 2b^2+11b-10=12+9b equation:

2b^2+11b-10=12+9b

We move all terms to the left:

2b^2+11b-10-(12+9b)=0

We add all the numbers together, and all the variables

2b^2+11b-(9b+12)-10=0

We get rid of parentheses

2b^2+11b-9b-12-10=0

We add all the numbers together, and all the variables

2b^2+2b-22=0

a = 2; b = 2; c = -22;
Δ = b2-4ac
Δ = 22-4·2·(-22)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{5}}{2*2}=\frac{-2-6\sqrt{5}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{5}}{2*2}=\frac{-2+6\sqrt{5}}{4}
$