4x(6x+8)=78

Solution for 4x(6x+8)=78 equation:

4x(6x+8)=78

We move all terms to the left:

4x(6x+8)-(78)=0

We multiply parentheses

24x^2+32x-78=0

a = 24; b = 32; c = -78;
Δ = b2-4ac
Δ = 322-4·24·(-78)
Δ = 8512
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:

$\sqrt{\Delta}=\sqrt{8512}=\sqrt{64*133}=\sqrt{64}*\sqrt{133}=8\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{133}}{2*24}=\frac{-32-8\sqrt{133}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{133}}{2*24}=\frac{-32+8\sqrt{133}}{48}
$