6(3x+6)4x=80

Solution for 6(3x+6)4x=80 equation:

6(3x+6)4x=80

We move all terms to the left:

6(3x+6)4x-(80)=0

We multiply parentheses

72x^2+144x-80=0

a = 72; b = 144; c = -80;
Δ = b2-4ac
Δ = 1442-4·72·(-80)
Δ = 43776
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:

$\sqrt{\Delta}=\sqrt{43776}=\sqrt{2304*19}=\sqrt{2304}*\sqrt{19}=48\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-48\sqrt{19}}{2*72}=\frac{-144-48\sqrt{19}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+48\sqrt{19}}{2*72}=\frac{-144+48\sqrt{19}}{144}
$