5*8^2x-3=320

Solution for 5*8^2x-3=320 equation:

5*8^2x-3=320

We move all terms to the left:

5*8^2x-3-(320)=0

We add all the numbers together, and all the variables

5*8^2x-323=0

Wy multiply elements

40x^2-323=0

a = 40; b = 0; c = -323;
Δ = b2-4ac
Δ = 02-4·40·(-323)
Δ = 51680
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:

$\sqrt{\Delta}=\sqrt{51680}=\sqrt{16*3230}=\sqrt{16}*\sqrt{3230}=4\sqrt{3230}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3230}}{2*40}=\frac{0-4\sqrt{3230}}{80}
=-\frac{4\sqrt{3230}}{80}
=-\frac{\sqrt{3230}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3230}}{2*40}=\frac{0+4\sqrt{3230}}{80}
=\frac{4\sqrt{3230}}{80}
=\frac{\sqrt{3230}}{20}
$