-11+3b(b+5)=7

Solution for -11+3b(b+5)=7 equation:

-11+3b(b+5)=7

We move all terms to the left:

-11+3b(b+5)-(7)=0

We add all the numbers together, and all the variables

3b(b+5)-18=0

We multiply parentheses

3b^2+15b-18=0

a = 3; b = 15; c = -18;
Δ = b2-4ac
Δ = 152-4·3·(-18)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-21}{2*3}=\frac{-36}{6}
=-6
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+21}{2*3}=\frac{6}{6}
=1
$