(8x+3)(2x+1)=9

Solution for (8x+3)(2x+1)=9 equation:

(8x+3)(2x+1)=9

We move all terms to the left:

(8x+3)(2x+1)-(9)=0

We multiply parentheses ..

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

We get rid of parentheses

16x^2+8x+6x+3-9=0

We add all the numbers together, and all the variables

16x^2+14x-6=0

a = 16; b = 14; c = -6;
Δ = b2-4ac
Δ = 142-4·16·(-6)
Δ = 580
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{145}}{2*16}=\frac{-14-2\sqrt{145}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{145}}{2*16}=\frac{-14+2\sqrt{145}}{32}
$