-11+b(2b+5)=7

Solution for -11+b(2b+5)=7 equation:

-11+b(2b+5)=7

We move all terms to the left:

-11+b(2b+5)-(7)=0

We add all the numbers together, and all the variables

b(2b+5)-18=0

We multiply parentheses

2b^2+5b-18=0

a = 2; b = 5; c = -18;
Δ = b2-4ac
Δ = 52-4·2·(-18)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-13}{2*2}=\frac{-18}{4}
=-4+1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+13}{2*2}=\frac{8}{4}
=2
$