3x(x+8)=x+4

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

3x(x+8)=x+4

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2+23x-4=0

a = 3; b = 23; c = -4;
Δ = b2-4ac
Δ = 232-4·3·(-4)
Δ = 577
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{577}}{2*3}=\frac{-23-\sqrt{577}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{577}}{2*3}=\frac{-23+\sqrt{577}}{6}
$