(8b+3)(2b-9)=16b-6

Solution for (8b+3)(2b-9)=16b-6 equation:

(8b+3)(2b-9)=16b-6

We move all terms to the left:

(8b+3)(2b-9)-(16b-6)=0

We get rid of parentheses

(8b+3)(2b-9)-16b+6=0

We multiply parentheses ..

(+16b^2-72b+6b-27)-16b+6=0

We get rid of parentheses

16b^2-72b+6b-16b-27+6=0

We add all the numbers together, and all the variables

16b^2-82b-21=0

a = 16; b = -82; c = -21;
Δ = b2-4ac
Δ = -822-4·16·(-21)
Δ = 8068
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:

$\sqrt{\Delta}=\sqrt{8068}=\sqrt{4*2017}=\sqrt{4}*\sqrt{2017}=2\sqrt{2017}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{2017}}{2*16}=\frac{82-2\sqrt{2017}}{32}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{2017}}{2*16}=\frac{82+2\sqrt{2017}}{32}
$