(3x+8)(8x+6)=46

Solution for (3x+8)(8x+6)=46 equation:

(3x+8)(8x+6)=46

We move all terms to the left:

(3x+8)(8x+6)-(46)=0

We multiply parentheses ..

(+24x^2+18x+64x+48)-46=0

We get rid of parentheses

24x^2+18x+64x+48-46=0

We add all the numbers together, and all the variables

24x^2+82x+2=0

a = 24; b = 82; c = +2;
Δ = b2-4ac
Δ = 822-4·24·2
Δ = 6532
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:

$\sqrt{\Delta}=\sqrt{6532}=\sqrt{4*1633}=\sqrt{4}*\sqrt{1633}=2\sqrt{1633}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-2\sqrt{1633}}{2*24}=\frac{-82-2\sqrt{1633}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+2\sqrt{1633}}{2*24}=\frac{-82+2\sqrt{1633}}{48}
$