(5x-4)(5x+4)=8x

Solution for (5x-4)(5x+4)=8x equation:

(5x-4)(5x+4)=8x

We move all terms to the left:

(5x-4)(5x+4)-(8x)=0

We add all the numbers together, and all the variables

-8x+(5x-4)(5x+4)=0

We use the square of the difference formula

25x^2-8x-16=0

a = 25; b = -8; c = -16;
Δ = b2-4ac
Δ = -82-4·25·(-16)
Δ = 1664
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:

$\sqrt{\Delta}=\sqrt{1664}=\sqrt{64*26}=\sqrt{64}*\sqrt{26}=8\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{26}}{2*25}=\frac{8-8\sqrt{26}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{26}}{2*25}=\frac{8+8\sqrt{26}}{50}
$