8x(4x+6)=18

Solution for 8x(4x+6)=18 equation:

8x(4x+6)=18

We move all terms to the left:

8x(4x+6)-(18)=0

We multiply parentheses

32x^2+48x-18=0

a = 32; b = 48; c = -18;
Δ = b2-4ac
Δ = 482-4·32·(-18)
Δ = 4608
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:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48\sqrt{2}}{2*32}=\frac{-48-48\sqrt{2}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48\sqrt{2}}{2*32}=\frac{-48+48\sqrt{2}}{64}
$