4x2-6=32x

Solution for 4x2-6=32x equation:

4x^2-6=32x

We move all terms to the left:

4x^2-6-(32x)=0

a = 4; b = -32; c = -6;
Δ = b2-4ac
Δ = -322-4·4·(-6)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{70}}{2*4}=\frac{32-4\sqrt{70}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{70}}{2*4}=\frac{32+4\sqrt{70}}{8}
$