4x2+2=82x

Solution for 4x2+2=82x equation:

4x^2+2=82x

We move all terms to the left:

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

a = 4; b = -82; c = +2;
Δ = b2-4ac
Δ = -822-4·4·2
Δ = 6692
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:

$\sqrt{\Delta}=\sqrt{6692}=\sqrt{4*1673}=\sqrt{4}*\sqrt{1673}=2\sqrt{1673}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{1673}}{2*4}=\frac{82-2\sqrt{1673}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{1673}}{2*4}=\frac{82+2\sqrt{1673}}{8}
$