3x(x+8)-2=4x+1

Solution for 3x(x+8)-2=4x+1 equation:

3x(x+8)-2=4x+1

We move all terms to the left:

3x(x+8)-2-(4x+1)=0

We multiply parentheses

3x^2+24x-(4x+1)-2=0

We get rid of parentheses

3x^2+24x-4x-1-2=0

We add all the numbers together, and all the variables

3x^2+20x-3=0

a = 3; b = 20; c = -3;
Δ = b2-4ac
Δ = 202-4·3·(-3)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{109}}{2*3}=\frac{-20-2\sqrt{109}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{109}}{2*3}=\frac{-20+2\sqrt{109}}{6}
$