5(5x+2)8x=20

Solution for 5(5x+2)8x=20 equation:

5(5x+2)8x=20

We move all terms to the left:

5(5x+2)8x-(20)=0

We multiply parentheses

200x^2+80x-20=0

a = 200; b = 80; c = -20;
Δ = b2-4ac
Δ = 802-4·200·(-20)
Δ = 22400
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:

$\sqrt{\Delta}=\sqrt{22400}=\sqrt{1600*14}=\sqrt{1600}*\sqrt{14}=40\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-40\sqrt{14}}{2*200}=\frac{-80-40\sqrt{14}}{400}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+40\sqrt{14}}{2*200}=\frac{-80+40\sqrt{14}}{400}
$