4x(3x-7)=32

Solution for 4x(3x-7)=32 equation:

4x(3x-7)=32

We move all terms to the left:

4x(3x-7)-(32)=0

We multiply parentheses

12x^2-28x-32=0

a = 12; b = -28; c = -32;
Δ = b2-4ac
Δ = -282-4·12·(-32)
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{145}}{2*12}=\frac{28-4\sqrt{145}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{145}}{2*12}=\frac{28+4\sqrt{145}}{24}
$