3(x+2)5x=6+8

Solution for 3(x+2)5x=6+8 equation:

3(x+2)5x=6+8

We move all terms to the left:

3(x+2)5x-(6+8)=0

We add all the numbers together, and all the variables

3(x+2)5x-14=0

We multiply parentheses

15x^2+30x-14=0

a = 15; b = 30; c = -14;
Δ = b2-4ac
Δ = 302-4·15·(-14)
Δ = 1740
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:

$\sqrt{\Delta}=\sqrt{1740}=\sqrt{4*435}=\sqrt{4}*\sqrt{435}=2\sqrt{435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{435}}{2*15}=\frac{-30-2\sqrt{435}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{435}}{2*15}=\frac{-30+2\sqrt{435}}{30}
$