32x+2+8x^2-6=92

Solution for 32x+2+8x^2-6=92 equation:

32x+2+8x^2-6=92

We move all terms to the left:

32x+2+8x^2-6-(92)=0

We add all the numbers together, and all the variables

8x^2+32x-96=0

a = 8; b = 32; c = -96;
Δ = b2-4ac
Δ = 322-4·8·(-96)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-64}{2*8}=\frac{-96}{16}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+64}{2*8}=\frac{32}{16}
=2
$