4(2x^2)=82

Solution for 4(2x^2)=82 equation:

4(2x^2)=82

We move all terms to the left:

4(2x^2)-(82)=0

a = 42; b = 0; c = -82;
Δ = b2-4ac
Δ = 02-4·42·(-82)
Δ = 13776
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:

$\sqrt{\Delta}=\sqrt{13776}=\sqrt{16*861}=\sqrt{16}*\sqrt{861}=4\sqrt{861}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{861}}{2*42}=\frac{0-4\sqrt{861}}{84}
=-\frac{4\sqrt{861}}{84}
=-\frac{\sqrt{861}}{21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{861}}{2*42}=\frac{0+4\sqrt{861}}{84}
=\frac{4\sqrt{861}}{84}
=\frac{\sqrt{861}}{21}
$